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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+aThen prove that a (1/b + 1/c ) , b (1/c + 1/a ), c (1/a + 1/b ) are in AP

Find the sum to n terms of the series :- 5 + 11 + 19 + 29 + 41 +..........

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}

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

_{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 = ?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

calculate the least no of terms of gp 5+10+20+...whose sum would exceed1000000

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

( answer = 1024 )

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

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.

ind the sum of n terms of :- 1/2*5+1/5*8+1/8*11+........

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.

if AM between two numbers exceeds their GM by 2 and the ratio of two numbers is 4, find the numbersThe sum of 11 terms of an AP whose middle term s 30 is

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

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

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 p

^{th},q^{th}and r^{th}terms of a G.P. are themselves in G.P.,show that p,q,r are in A.P.how many terms of the sequence 18,16,14......should be taken so that their sum is zero.

Which term of the sequence 8-6i,7-4i,6-2i,...... is (i) purely real (ii) purely imaginary?

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.the sum of all possible products of first n natural numbers taken two at a time is

ANS:(1/24)*n(n+1)(n-1)(3n+2)

If

a,b,c,dare in G.P, prove that are in G.P.if sum of 40 A.Ms between two numbers is 120,find the sum 50 AMs between them.

find the sum of integers from 1 to 100 that are divisible by 2 or 5?

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

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.

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?

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}In an A.P.,s

_{3}=6,s_{6}=3,prove that 2(2n+1)S_{n}_{+4}=(n+4)S_{2n+1}.^{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.

Find the sum to

nterms of the sequence, 6, 66, 666, 6666…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 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

In an A.P. the sum of the terms equidistant from the beginning and end is always same and equal to the sum of first and last terms.

If in an A.P., S

_{n}= n^{2}p and S_{m}=m^{2}p, then S_{p}=?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 )

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

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

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.

find the general term of progression 1/4,-1/2,1,-2....

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

THE THIRD TERM OF A G.P IS 2/3 & THE 6TH TRERM IS 2/81 FIND THE 8TH TERM

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 (b-c)^2, (c-a)^2, (a-b)^2 are in AP prove that 1/(b-c) , 1/(c-a) , 1/(a-b) are in AP.

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).

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}If

a,b,care in GP, prove thata

^{2}b^{2}c^{2}[ ( 1 / a^{3}) + ( 1 / b^{3}) + ( 1 / c^{3}) ] = a^{3}+ b^{3}+ c^{3}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.....!!

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?

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

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.

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

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

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

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?