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Syllabus

The ratio of the sum of n terms of two A.P.s is (7n+1):(4n+27).Find the ratio of their mth term.

if 1+2+3+..............+n = 666, find the value of n.

^{2 }: n^{2.}show that the ratio of the m^{th}and n^{th}terms is (2m-1) : (2n-1)^{2}/2 + 5n/2, find its 25^{th }term.The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last terms to the product of the two middle terms is 7 : 15. Find the numbers.If the m

^{th}term of an A.P. be 1/n and n^{th}term be 1/m, then show that its (mn)^{th}term is 1.IF THE SUM OF FIRST m TERMS OF AN AP IS n. AND THE SUM OF FIRST n TERMS IS m, THEN SHOW THAT THE SUM OF ITS FIRST( m+n) TERMS IS -(m+n).

If S

_{n }=(3n^{2}+2n) , find the first term and the common difference of the AP.Maths Project :make designs using arithmetic progression

if 3x+k,2x+9 and x+13 are three consecutive terms of an AP.,Find k.if the pth term of an A.P is q and the qth term is p, prove that its nth term is (p+q-n)

A B set out to meet each other from two places 165 km apart. 'A' travels 15 km the first day, 14 the second day, 13 the third day and so on. 'B' travels 10 Km the first day, 12 Km the second day, 14 the third day and so on. After how many days they will meet each other.

the sum of the first n terms of an AP is given by s

_{n}=3n^{2}-n , determine the AP and its 25^{th}term.Find four numbers in A.P such that their sum is 16 and their product is 105.

If m times the mth term of an A.P is equal to n times its nth term, show that the (m+n)th term of the A.P is zero.

the sum of first six terms of an ap is 42 .the ratio of its 10th term is and its 30th term is 1:3. calculate the first and thirteenth term

The sum of the third and seventh term of an A.P. is 6 and their product is 8. Find the sum of the first sixteen terms of the A.P. .

If pth , qth and rth term of an AP are a,b,c respectively , then show that

(a-b)r +(b-c)p + (c-a)q = 0

Please help me with this question asap .

150 workers were engaged to finish a piece of work in a certain no. of days. 4 workers droped d 2nd day, 4 more workers droped the 3rd day n so on..... it takes 8 more days to finish the work now ..find d no. of days in vch the work waz completed....

8. In 4ABC, A = 25

An AP consists of 37 terms. The sum of the three middle most terms is 225 and the

If the sum of first 7 terms of an AP is 49 and that of first 17 terms is 289.Find the sum of first n terms

The sum of n terms of two ap are in ratio (5n+4) : (9n+6) Find the ratio of their 18th term?

plzz reply with solution

how many terms of an a.p. -10,-7,-4....... must be added to get the sum 104?

if m times mth term of an Ap is equal to n times nth term, find its (m+n)th term...PLZ ANSWER IT SOON......the ratio of the sum of n terms of two AP's is (7n+1):(4n+27).find the ratio of their m th terms.

Answer: let a1 , a2 be the 1st terms and d1 , d2 the common differences of the two given A.P's. then the sums of their n terms are given by

Sn = n/2 {2.a1+(n-1)d1} and Sn' = n/2{2. a2 +(n-1)d2}

Sn/Sn' = n/2{2.a1+(n-1)d1} / n/2{2.a2 + (n-1)d2}

Sn / Sn' = 2.a1+(n-1)d1 / 2.a2 + (n-1)d2

it is given that

Sn / Sn' = 7n+1 / 4n + 27

2.a1 + (n-1)d1 / 2.a2 + (n-1)d2 = 7n+1 / 4n+27 ........................ (i)

To find the ratio of the mth terms of the two given AP's , we replace n by (2m-1) in equation (i)

therefore, 2.a1 + (n-1)d1 / 2.a2 + (n-1)d2 = 7(2m-1) + 1 / 4(2m-1) + 27

a1 + (m-1)d1 / a2 + (m-1)d2 = 14m - 6 / 8m + 23

Hence, the ratio of the mth terms of the two A.P's is (14m - 6) : (8m + 23)

My question is, why it has been assumed (2m-1) in the place of 'n' ? has it been arrived from solving with the help of a formula or is it a mere assumption? if it is simply an assumption, why it should be assumed as (2m-1) ? why not 2m or (m - 1)

Q.135. If a

_{1}, a_{2}, a_{3}, .... is an arithmetic progression with common difference 1 and $\sum _{\text{i=1}}^{98}{\text{a}}_{1}\text{=137,}\phantom{\rule{0ex}{0ex}}$ then the value of a_{2}+ a_{4}+ a_{6}+ ......+ a_{98}is(1) 67

(2) 83

(3) 93

(4) 98

If s

_{n}, the sum of first n terms of an AP is given by s_{n}= (3n^{2}-4n), then find its nth term.Let

Tbe the_{r}th term of an A.P. IfrmT=_{m}nT_{n}, then show thatT= 0_{m+n}If the sum of m terms of an A.P is the same as the sum of n terms of the same A.P, show that the sum of its (m+n) terms is zero.

Q.1. What is the missing number in the pie below?

what are the uses of arithmetic progressions in daily life? i want atmost 10, pls help me as soon as possible

if the nth term of an AP is (2n+1) find the sum of first n terms of the AP

_{1}, A_{2}are two AMs between two numbers a and b, then (2A_{1}- A_{2}) ( 2A_{2}- A_{1}) is equal to(A) a + b (B) $\frac{ab}{a+b}$ (C) ab (D) $\frac{a+b}{ab}$

sum of first p , q and r terms of an A.P. are a , b and c respectively. Prove that :

a/p (q-r) + b/p(r-p) + c/r (p-q) = 0

If S

_{1}, S_{2}, S_{3}are the sum of n terms of three AP's the first term of each being unity and respective common diffrence being 1 , 2 , 3_ _ _ _ _. Prove that S_{1}+S_{3}= 2S2.which term of an AP 3,15,27,39............ will 132 more than its 54

^{th}termDivide 56 into 4 parts which are in AP such that hte ratio of product of extremes to the product of mean is 5 : 6? Hoping for a quick response......plz.....[ May be within Sunday ]

14. The sequence a

_{1, }a_{2}, a_{3}, ......a_{98}satisfies the relation a_{n+1}= a_{n}+1 for n = 1, 2, 3, ...., 97 and has the sum equal to 4949, then, evaluate $\sum _{k=1}^{49}{a}_{2k}.$if sum of n terms of an AP 2n

^{2}+ 5n, then find its n^{th}term.In an AP,the sum of first n term is 3n2/2+13n/2

find its 25th term

solve the solution 1+4+7+10.............+x = 287

What is the maning of the sentence - Why are you freaking nuts ?

if Sn denotes the sum of first n terms of an A.P., prove that S12=3(S8-S4).

if 1/x+2 , 1/x+3 , 1/x+5 are in AP then find x.

the sum of 4th and 8th terms of an AP is 24 and the sum of 6th and 10th terms is 44. find the first 3 terms of the AP.

Divide 32 into 4 parts which are in A.P. such that the product of extremes is to the product of means is 7:15.

^{n}c_{1,}^{n}c_{2 }and^{n}c_{3}will be in arithmetic progression?30) the digits of a positive integer,having three digits are in A.P. and their sum is 15.the number obtained by reversing the digits is 594 less than the original number.find the number.

Find the LCM of (x + 3)(6x

^{2}+ 5x+ 4) and (2x^{2}+ 7x + 3) (x + 3)(2x + 1) (x + 3) (3x + 4)

(4x

^{2}– 1) (x + 3)^{2}(3x + 4)(4x

^{2}– 1) (x + 3) (3x + 4)(2x – 1) (x – 3) (3x + 4)

Hint:Find the sum of all the integers between 100 and 200 that are not divisible by 9

write the ap whose second term is 13 and the difference of the 4th term from the 8th term is 16.

In an AP of 50 terms, the sum of first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the A.P.4. Find a, b and c such that the following numbers are in AP: a, 7, b, 23, c. 5. Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20. 6. The 26th, 11th and the last term of an AP are 0, 3 and 1 – 5 , respectively. Find the common difference and the number of terms.

7. The sum of the 5th and the 7th terms of an AP is 52 and the 10th term is 46. Find the AP.

8. Find the 20th term of the AP whose 7th term is 24 less than the 11th term, first term being 12.

9. If the 9th term of an AP is zero, prove that its 29th term is twice its 19th term.

10. Find whether 55 is a term of the AP: 7, 10, 13,--- or not. If yes, find which term it is. ARITHMETIC PROGRESSIONS 53 11. Determine k so that k2 + 4k + 8, 2k2 + 3k + 6, 3k2 + 4k + 4 are three consecutive terms of an AP.

12. Split 207 into three parts such that these are in AP and the product of the two smaller parts is 4623. 13. The angles of a triangle are in AP. The greatest angle is twice the least. Find all the angles of the triangle. 14. If the nth terms of the two APs: 9, 7, 5, ... and 24, 21, 18,... are the same, find the value of n. Also find that term. 15. If sum of the 3rd and the 8th terms of an AP is 7 and the sum of the 7th and the 14th terms is –3, find the 10th term. 16. Find the 12th term from the end of the AP: –2, –4, –6,..., –100. 17. Which term of the AP: 53, 48, 43,... is the first negative term? 18. How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?

19. Find the sum of the two middle most terms of the AP: 4 – 3 , –1, 2 – 3 ,..., 1 4 3 . 20. The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference. 21. Find the sum: (i) 1 + (–2) + (–5) + (–8) + ... + (–236) (ii) 1 4 – n + 2 4 – n + 3 4 – n +... upto n terms (iii) – 3 –2 5 –3 ... ab a b a b ab ab ab + ++ ++ + to 11 terms. 22. Which term of the AP: –2, –7, –12,... will be –77? Find the sum of this AP upto the term –77. 23. If an = 3 – 4n, show that 12 3 aaa , , ,... form an AP. Also find S20 .

24. In an AP, if

Sn = n (4n + 1), find the AP. 25. In an AP, if Sn = 3n2 + 5n and ak = 164, find the value of k. 26. If Sn denotes the sum of first n terms of an AP, prove that S12 = 3(S8 –S4 ) 27. Find the sum of first 17 terms of an AP whose 4th and 9th terms are –15 and –30 respectively.

28. If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.

29. Find the sum of all the 11 terms of an AP whose middle most term is 30.

30. Find the sum of last ten terms of the AP: 8, 10, 12,---, 126. 31. Find the sum of first seven numbers which are multiples of 2 as well as of 9. [Hint: Take the LCM of 2 and 9]

32. How many terms of the AP: –15, –13, –11,--- are needed to make the sum –55? Explain the reason for double answer.

33. The sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another AP whose first term is – 30 and the common difference is 8. Find n. 34. Kanika was given her pocket money on Jan 1st, 2008. She puts Re 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?

35. Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?

A

contractoremployed150 labourersto finish a peice of work in a certain no. of days.4 workerswent away thesecond day,4 more workerswent away thethird dayandso on. Ifit took 8 more daysto finish the work ,find the no. of days in which the work was completed.

ANURAG.Rs 4800 becomes Rs 6000 in 4 years at a certain rate of compound interest. What will be the sum after 12 years ?

9375 Rs.

9000 Rs.

9175 Rs.

8175 Rs

The sum of n 2n 3n terms of an AP are S1 S2 S3 respectively. Prove that S3=3(S2-S1).

the nth term of an AP is given by a

_{n}= 4n - 5,then find the sum of first 25 terms of the AP.Find the sum of first five multiples of 3?

Which term of AP:121,117,113,......., is its first negative term?

find the sum of all the natural numbers between 200 and 300 which are divisible by 4.

help plsss

how many terms of an AP must be taken for their sum to be equal to 120 if its third term is 9 and the difference between the seventh and second term is 20

The angles of a quadrilateral are in a.p. whose common difference is 10degree.Find the angles.

FIND the 4th term from the end of the A.P. ................ 2 , 5 , 8 ................ , 35If there are (2n+1) terms in A.P,then prove that the ratio of the sum of odd terms and the sum of even terms is (n+1):n.

THe sum of the first n terms of an AP is 5n square - n square. Find thenth term of this AP

Find the 20th term from the last term of the AP 3, 8, 13, .....253.

If s

_{n }denotes the sum of n terms of AP whose common difference is d and first term is a, find s_{n}-2s_{n-1}+s_{n-2}Find the middle term (s) in the A.P. 20,16,12,.........-176.

Show that sum of an AP whose first term is a,the second term b and the last term c,is equal to (a+c)(b+c-2a)/2(b-a)..Plzzz i need hlpp!!!!

if the Pth term of an AP is Q and its Qth term is P then show that its (P+Q)th term is zero/

^{2}-n. find out the first term and the common difference.The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.

in an AP,the sum of first ten terms is -150 and the sum of its next ten terms is -550.Find the AP.

if sn denotes the sum of first n trems of an ap, prove that s12=3(s8-s4)

find the 6th term from end of the A.P: 17,14,11....-40

THE ANGLES OF A TRIANGLE ARE IN A.P.THE GREATEST ANGLE IS TWICE THE LEAST.FIND ALL THE ANGLES OF THE TRIANGLE.