if a², b²,c² 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

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

( answer = 1024 )

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

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

the sum of n terms oof two ap are in the ratio(7n-5) :(5n+17).Show

that their 6th term are equal.

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?

The sum of four distinct numbers in G.P is 60 and  the arithmetic mean of the first and the last is 18. Find the numbers.
 

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

If a,b,c are in A.P. and a,b,d are in G.P. ,prove that a,a-b,d-c are in G.P.

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.

1. if G is the G.M between a and b show that

1G²-a²+1/G²-b²⁼1/G²

2 find n such that aⁿ+bⁿ/a^n-1+b^n-1 may be the geometric mean between a and b

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.

pls answer-- in an AP if a_p+1 = 2a_q+1 prove that a_3p+1 = 2a_p+q+1..

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

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

 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

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 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) .

Sum the series: [(sqrt 2) + 1] +1 + [(sqrt 2 -1) + ..... upto infinity.

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

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 a, b, c, d are in G.P, prove that are in G.P.

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}

if p^th, q^th, r^thand 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.

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

Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7^th and (m – 1)^th numbers is 5:9. Find the value of m.

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

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

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

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

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)

1. If a,b,c are in A.P and X,Y,Z are in G.P then prove( X^b-c)x (Y^c-a) x(Z^a-b)=1
2. In a G.P t_p+q=m and t_p-q=n. Then find t_p.

Find the sum of n terms of the sequence

( x + 1/x )² , ( x² +1 /x²)²  , (x³  + 1/x³ )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.

Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.

Find the sum tonterms of the sequence, 6, 66, 666, 6666…

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

If in an A.P., S_n= n²p and S_m=m²p, then S_p=?

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 pth term of a gp is p and qth term is q.prove that the nth term is (p (to the power n-q) /q (to the power n-p) ) to the power 1/p-q

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

1+2x+3x²+4x³..........to infinity

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

show that in an infinite gp each terms bears a constant ratio to the sum of all the terms that follow it.

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.

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 ??

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.

Sum to infinity of following series??

(2/3) - (5/6) + (2/3) - (11/24) + ...............

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

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 a, b and c are in A.P. then prove that (1/root b + root c), (1/root c + root a) + (1/root a + root b) are in A.P.

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).

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

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 P²Rⁿ = Sⁿ

In an A.P.,s₃=6,s₆=3,prove that 2(2n+1)S_n+4=(n+4)S_2n+1.

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

find the sum of the following series to n terms: (i) 3+5+9+15+23_ _ _

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.....

Find the sum the following series to n terms:

  3+7+14+24+37+.........

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

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

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

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 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?

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

plz ans fast....

its very urgent

if the sum of n terms of an A.P. is (pn+qn2), where p&q are constants, find the common difference.

If pth,qth,rth and sth terms of an A.P. are in G.P.,then show that (p-q),(q-r),(r-s) are also in G.P.(example of ncert).

plzzz explain it couldn't understand !!