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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+aIf 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

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

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

( answer = 1024 )

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

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

pls answer-- in an AP if a

_{p+1}= 2a_{q+1 }prove that a_{3p+1}= 2a_{p+q+1..}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.

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

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

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

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

Find the sum of n terms of the sequence

( x + 1/x )

^{2}, ( x^{2}+1 /x^{2})^{2}, (x^{3}+ 1/x^{3})^{2},..........Sum the series: 1+3+7+15+31+............to n terms.

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

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 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 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.

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

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

Between 1 and 31,

mnumbers 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 ofm.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+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: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

^{b-c})x (Y^{c-a}) x(Z^{a-b})=1_{p+q}=m and t_{p-q}=n. Then find t_{p}.1. if G is the G.M between a and b show that

1G

^{2}-a^{2}+1/G^{2}-b^{2=}1/G^{2}2 find n such that a

^{n}+b^{n}/a^{n}^{-1}+b^{n-1 }may be the geometric mean between a and bIf 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}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…ind the sum of n terms of :- 1/2*5+1/5*8+1/8*11+........

If in an A.P., S

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

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

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

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)

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.

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

that their 6th term are equal.

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

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.

1+2x+3x

sum of this series^{2}+4x^{3}..........to infinityIn 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.

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.

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 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 sides of a right angled triangle are in ap show that the sides are in the ratio 3:4:5 ?

Please reply soooooooooooooooooooooon

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 }= 2ALet 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 x1,x2,x3 ....xn are in H.P then prove that x1x2+x2x3+x3x4+....+xn-1xn =( n-1)x1xn

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.....

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

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

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

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?

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

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

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

plz ans fast....

its very urgent

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 !!

If a,b,c are in AP as well as in GP then show that a=b=c.