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

Q3.A person was drawing a monthly salary of Rs 2500 in 11th year of servce and a salary of Rs 2900 in the 19th year. Given that pension is half the salary at retirement time, find his monthly pension if he had put in 25 years of service before retirement. Assume that annual increment is constant.

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

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

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

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

( answer = 1024 )

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

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

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.

_{e}(1-x))/x^{3}isIf 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

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

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

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

Evaluate 3. 3

^{1/2}. 3^{1/4}. 3^{1/8}. ................... upto infinity.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) .

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

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

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

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._{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 = ?If

a,b,c,dare in G.P, prove that are 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?

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

Find two numbers whose difference is 2 and whose AM exceeds the GM by 1/2.Âprove that:2^1/4 . 4^1/8 . 8^1/16............upto infinity=2

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

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.

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}if sum of 40 A.Ms between two numbers is 120,find the sum 50 AMs between them.

^{b-c})x (Y^{c-a}) x(Z^{a-b})=1_{p+q}=m and t_{p-q}=n. Then find t_{p}.is 0,0,0,...0 an arithmetic progression

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

find the sum of the first 25 trrms of the series 5.6+6.7+7.8+.....

Find the sum to

nterms of the sequence, 6, 66, 666, 6666…Find the sum to n terms of the series 1x3x5+3x5x7+5x7x9+....

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}=?2.1+3.2+4.4+5.8+.....

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

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

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

write the value of n if the sum of n terms of the series 1+3+5+7................to n terms is n^2

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

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.

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.

^{th}mean: n^{th}mean is 11:24, then find 'n'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: a+b/2,a,3a-b/2,.... to 21 terms

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

pls answer-- in an AP if a

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

If the sum of n terms of an A.P. is 2mn + pn

^{2}, where m and p are constants, find the common differencethe 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 the sum of first four terms of an AP IS P AND THE SUM OF FIRST 8 TERMS IF IS Q AND SUM OFfirst 12 terms is r. express 3p+r in terms of q

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.....

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 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

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

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

If G1 is the first of n GMs between two positive numbers a and b , then show that G1 to the power n+1 = a tothe power n*b.

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

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.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.

(xbe the A.M between x and y, then find the value of p.^{p}+ y^{p})/ (x^{p-1}+ y^{p-1})The sum of the infinite G.P is 15, Sum of squares of 3 terms of the g.p is 45. Find the series.

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

plz ans fast....

its very urgent

?, 20, 36, 68, 132, 260

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 ??