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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.

^{1/n}-n (B)greater than or equal to n(n+1)^{1/n}/(n+5) (C)less than n(n+1)^{1/n}- n (D) equal to n(n+1)^{1/n}- na 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

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

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

( answer = 1024 )

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

If the sum of n terms of an AP is given by S

_{n}=(3n^{2}+4n),find the r^{th }term.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.

find the number of terms in the A.P. 3,7,11,........407.Also find 20th term from the end

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

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

2.3^2 +5.4 ^2 +8.5^2

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 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) .

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

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

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

The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.

$\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+......n$

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

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

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}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

^{b-c})x (Y^{c-a}) x(Z^{a-b})=1_{p+q}=m and t_{p-q}=n. Then find t_{p}.If

a,b,care in AP, prove thata.^{3}+ 4b^{3}+ c^{3}= 3b ( a^{2}+ c^{2})Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.

$2.Ifxyz=\left(1-x\right)\left(1-y\right)\left(1-z\right)where0\le x,y,z\le 1,thentheminimumvalueofx\left(1-z\right)+y\left(1-x\right)+z\left(1-y\right)is:\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(a\right)\frac{3}{2}\left(b\right)\frac{1}{4}\left(c\right)\frac{3}{4}\left(d\right)\frac{1}{2}$

Find the sum to

nterms of the sequence, 6, 66, 666, 6666…solve the equation 2+5+8...+x=155

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 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 in an A.P., S

_{n}= n^{2}p and S_{m}=m^{2}p, then S_{p}=?calculate the least no of terms of gp 5+10+20+...whose sum would exceed1000000

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

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

The nth term of a geometric progression is 2^n-1/3 for all values of n. Write down the numerical values of the first three terms and calculate the sum of the first 10 terms, correct to 3 significant figures

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

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

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.

what do you mean by term partial fraction ? explain it

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.

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

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

?, 20, 36, 68, 132, 260

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.

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

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 }= 2Aif 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).

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.....

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}Find the sum of 30th term of the sequence 7, 7.7, 7.77, 7.777..................

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

let 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.....!!

Find the sum of the series 2+11+101+1001+… to n terms.

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

find four numbers in GP whose sum is 85 and the product is 4096.

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.

The sum of the infinite G.P is 15, Sum of squares of 3 terms of the g.p is 45. Find the series.

a man was pointed in the grade of rs.7000-400-15000.in which year of his service will he be drawing salary of rs.10200

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

plz ans fast....

its very urgent

(xbe the A.M between x and y, then find the value of p.^{p}+ y^{p})/ (x^{p-1}+ y^{p-1})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 ??

Q 9

9. Sum up 3+5+11+29.........to n terms.