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Syllabus

if a

^{2}, b^{2},c^{2 }are in a A.P .then prove that the following are also in A.P (i) 1/b+c ,1/c+a ,1/a+b (ii) a/b+c , b/a+c ,c/b+a_{k}a_{k-1 }+ a_{k-1}a_{k-2} = 2a_{k}a_{k-2 }, k>=3 and a_{1}=1 , here S_{p}= sigma (k = 1 to k = p) 1/a_{k }and given that S_{2p}/S_{p }does not depend on p then 1/a_{2016 }is = ?Find the sum to n terms of the series :- 5 + 11 + 19 + 29 + 41 +..........

sum the series

3.8+6.11+9.14+...to n terms

Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

the first term of the GP is 85, the sum of second term of AP and the second term of the GP is

76 and that of the 3rd term of AP and 3rd term of GP is 84. The sum of the AP is 126. Find each

term of AP and GP

a thief runs away from a police station with a uniform speed of100 m per min. after a minute a policeman runs behind him to catch. he goes at a speed of 100 m in 1

^{st }min and increases his speed by 10 m each succeeding min. after how many min, the policeman catch the thief?If the pth, qth and rth terms of a GP be a, b, c respectively, prove that

a^(q-r).b^(r-p).c^(p-q)=1;

where ^=raised to the power

a machine depreciates in value at the rate of 30% every year in the reducing balance. if the original cost be rs 20000 and ultimate scrap value be rs 4802. find the effective life of the machine.

The third term of a GP is 4 , find the product of its first five terms .

( answer = 1024 )

1) if a=-7, r=7/2, find t6

2) if t8=640, r=2, find a

Q2) find 3 nos. In GP such that their sum is 13/3 and the sum of their sequence is 91/9

Q3) for GP 0.03, 0.06, 0.08,.... Find Sn

Q4) for GP if t3=36, t6=972, find S4

Q5) insert 2 nos. Between 4 and 32, so that resulting sequence is a GP

If a2, b2, c2, are in AP, then show that a/b+c, b/c+a, c/a+b are in AP.

if x1,x2,x3 ....xn are in H.P then prove that x1x2+x2x3+x3x4+....+xn-1xn =( n-1)x1xn

if (m+1)th term of an AP is twice the n+1th term, prove that (3m+1)th term is twice the (m+n+1)th term.

please answer ASAP, exam tmrw.

If 7 times the 7th term of an A.P. is equal to 11 times the 11th term,show that 18th term of A.P. is 0.

The first term of an AP is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.

The sum of 11 terms of an AP whose middle term s 30 is

(1) 320 (2)330 (3)340 (4)350

7^2+9^2+11^2+............n terms

Sum the series: 1+3+7+15+31+............to n terms.

If a, b , c are in G.P, and x, y be the arithmetic means of a, b and b, c respectively, prove that (i) a/x+c/y=2 (ii)1/x + 1/y= 2/b

if tan(alpha+theta) = ntan (alpha-theta) then show that : (n+1)sin 2theta=(n-1)sin 2alpha

If first term ,second , and last term of an A.P be a ,b , c, respectively . Then show that the sum is

(b+c-2a) (a+c) / 2(b-a) .

how many terms of the sequence 18,16,14......should be taken so that their sum is zero.

the sum of first n terms of the series 1square + 2* 2square + 3square +2*4square + 5square + 2*6square +... is n*(n+1)square/2 when n is even. What is the sum when is odd?

if p

^{th}, q^{th}, r^{th}and s^{th}terms of an A.P. are in G.P.,show that (p-q),(q-r) and (r-s) are also in G.P.If 1/x,1/y,1/z are AP, show that:

(i) yz,zx,xy are in AP

(ii) xy,zx,yz are in AP

(iii) y+z/x,z+x/y,x+y/z are in AP

I got the first one but how to do the other two?

If

a,b,c,dare in G.P, prove that are in G.P.find the sum of integers from 1 to 100 that are divisible by 2 or 5?

19. Consider a three digit number x

_{1}x_{2}x_{3}such that x_{1}.x_{2}.x_{3}$\in $ N. Then the number of positive integral solutions of x_{1}.x_{2}.x_{3 }= 480 is ${\lambda}^{2}$ -100, then the sum of the digits of $\left|\lambda \right|$ is(A) 8 (B) 9 (C) 7 (D) 10

prove that:2^1/4 . 4^1/8 . 8^1/16............upto infinity=2

If a

^{2}+2bc,b^{2}+2ac,c^{2}+2ab are in A.P. ,show that 1/(b-c),1/(c-a),1/(a-b) are also in A.P.The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.

let x=1+a+a2+.............. y=1+b+b2+.......... thn prove that

1+ab+a2b2+.......=xy/x+y-1

How many different words can be formed of the letters of the word 'MALENKOV' so that:

1) No two vowels are together.

2) The vowels may occupy odd places

If the p

^{th},q^{th}terms of a G.P. are q,p respectively ,show that (p+q)^{th}term is (q^{p}/p^{q})^{1/p-q}If the 5th term of an A.P. is 1/10 and the 10th term is 1/5 then find the 50th term of an A.P.

^{b-c})x (Y^{c-a}) x(Z^{a-b})=1_{p+q}=m and t_{p-q}=n. Then find t_{p}.Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.

If a constant is multiplied to each term of an A.P., the resulting sequence will also be an A.P.

If a constant is divided from each term of an A.P., the resulting sequence will also be an A.P.

This is written in the study material but in these two cases the common difference is not constant then how these are A.P. PLZ. ANS. FAST...Find the sum to

nterms of the sequence, 6, 66, 666, 6666…If 1/a, 1/b, 1/c are in AP, prove that (i) b + c / a, c +a / b, a + b / c are in AP (ii) a(b +c), b (c +a), c ( a + b) are in AP

If in an A.P., S

_{n}= n^{2}p and S_{m}=m^{2}p, then S_{p}=?find the number of terms in the A.P. 3,7,11,........407.Also find 20th term from the end

1+(1+2)+(1+2+3)+(1+2+3+4)... find the sum of the series

If a+b+c not equal to zero and b+c/a,c+a/b,a+b/c are in AP.Prove that 1/a,1/b,1/c are also in AP

Show that a^2,b^2,c^2 are in AP if and only iff 1/b+c,1/c+a,1/a+b are in AP

{Experts can you please clarify my doubts}

a) 1/2 (root 5) b) root 5 c) 1/2 (root 5 - 1) d) 1/2 (1- root 5 )

FIND FOUR NUMBERS IN AP WHOSE SUM IS 20 &SUM OF WHOSE SQUARES IS 120

The sum of squares of the first n natural numbers is given by to prove it why we are taking cubes its squares right

The difference between any two consecutive interior angles of a polygon is 5°.If the smallest angle is 120°, find the number of the sides of the polygon.

the sum of 4 numbers in a.p is 40 and the product of their extremes is 91.the number are

In the arithmetic progression 2,5,8....upto 50 terms,and 3,5,7,9....upto 60 terms ,find how many pairs are identical and find the identical pairs.

solve the equation 2+5+8...+x=155

three numbers are in A.P. and their sum is 15 , if 1, 4 and 19 are added to these numbers respectively the resulting numbers are in G.P.. find the numbers.

The sum of an infinite number of terms of GP is 4 and the sum of their cubes is 192. Find the series.

In an A.P.,s

_{3}=6,s_{6}=3,prove that 2(2n+1)S_{n}_{+4}=(n+4)S_{2n+1}.The sum of first two terms of an infinite G.P. is 5 and each terms is three times the sum of the succeeding terms. Find the G.P.

Show that thesum of (

m+n)^{th}and (m-n)^{th}term of an A.P is equal to twice them^{th}term.?, 20, 36, 68, 132, 260

the sum of three numbers in GP is 56. if we subtract 1, 7, 21 from these numbers in that order, we obtain an AP. find the numbers.

If one A.M.,

Aand two geometric meansG_{1}_{ }andG_{2}_{ }inserted between any two positive numbers,show thatG._{1}^{2}/ G_{2}+ G_{22}/ G_{1 }= 2A100

Sigma 3

^{r}(2-2r)/(r+1)(r+2)r=2

Options : -

(A) 1/2 - {3

^{100}/100(101)}(B) 3/2 - {3

^{101}/101(102)}if in a gp the (p+q)th term is a and (p-q)th term is b , prove that the pth term is sqrt (ab).

2.1+3.2+4.4+5.8+.....

pth term of an A.P. is 'a' and qth term is 'b'. prove that sum of (p+q)th term is p+q/2[a+b+(a-b/p-q)]. plz ans needed soon.....

^{2}^{}+....... (till infinity) (mod of x < 1)Let S be the sum, P be the product and R be the sum of reciprocals of n terms in a G.P. Prove that P

^{2}R^{n}= S^{n}If S

_{n}denotes the sum to n terms of an A.P. and p^{2}S_{p}= pS_{p2}for each p∈ N then S_{n}is(A) depends on d only (B) divisible by n

^{2}(C) divisible by n (D) divisible by (n-1) .Give the process.Find the sum of 30th term of the sequence 7, 7.7, 7.77, 7.777..................

in an increasing GP , the sum of the first and the last term is 66 , the product of the second and the last but one term is 128 , and the sum of all the terms is 126. how many terms are there in the progression.

sum of an infinite gp is 57 and sum of their cube is 9747 find the gp

The sum of series 1/2! + 1/4! + 1/6! + ..... islet x=1+a+a^2........ and y=1+b+b^2..... , where modulus(a)

1+ab+a^2b^2.......=xy/(x+y-1)

please i have a test tommorow.....!!

Prove that a,b,c are in A.P. iff 1/bc,1/ca,1/ab are also in A.P.

find the sum of the following series:1

^{2}+3^{2}+5^{2}+..........to n terms.1.If the AM ,GM and HM of the first and last terms of the series 25,26,27,.....N-1,N are the terms of the series,find the value of N?

2.The sum of all possible products of the first 'N' natural numbers taken two bu two is:

a)1/24n(n+1)(n-1)(3n+2)

b)n(n+1)(n-1)(2n+3)/24

c)n(n+1)(n-1)(2n+1)/6

d) none of these

(where summation is from n=1 to n=20)

If p , q, r are in G.P and the equation px^2 + 2qx + r = 0 and dx^2 + 2ex + f = 0 have a common root , then show that d/p , e/q , f/r are in A.P.

what is the proof of formula : s

_{n=}n/2(2a=(n-1)dThe sum of the infinite G.P is 15, Sum of squares of 3 terms of the g.p is 45. Find the series.

(A)15 (B)48 (C)44 (D)42

Find the sum of sequence, 7, 77, 777, 7777..... to n terms ???

plz ans fast....

its very urgent

5+55+555...n terms. Change this term into G.P. then find the sum of this series?

If (a1,a2,a3......an) are in A>P> with common difference d. then the sum of the series: sin d [cosec a1.cosec a2 + cosec a2.cosec a3 +........+ cosec a(n-1).cosec an ] is what ??

if p arithmetic means are inserted between a and b, prove that d=b-a/p+1