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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+athe 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)

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.

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

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?2.5 + 5.8 + 8.11+ ....... n terms find d sum

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 )

The first term of an AP is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.

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.

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 (b+c-a)/a , (c+a-b)/b & (a+b-c)/c are in A.P., then prove that 1/a, 1/b & 1/c are also in A.P. ...... answer urgently needed!!

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

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

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

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

sum of series 1.2^2 + 3.3^2 + ..................n terms

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) .

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

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

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

^{2}, 1/b^{2}, 1/c^{2}are in A.P, prove that -a/2, b,c are in G.P or else a=b=cThe sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.

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

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

^{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.

^{2}=(x-c)(x-a)Find the sum to

nterms of the sequence, 6, 66, 666, 6666…if the sum of n terms of a gp is 255 and nth terms is 128 and common ratio is 2, then first term will be?

if the roots of cubic equation ax cube + bx square + cx + d = 0 are in gp then

option1. c cube a = b cube d

2. c a cube =b d cube

3. a cube b = c cube d

4. ab cube = cd cube

which one of the following option will b correct

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

that their 6th term are equal.

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 the sum of the series : 1 + (1/3) + (1.3/3.6) + (1.3.5/3.6.9) + ........... infinity. ( notation dot (.) here implies multiplication)

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.

given that n arithmetic means are inserted between two sets of numbers a, 2b and 2a, b where a, b are real numbers . suppose further that mth mean between these two sets of numbers is same then the ratio a : b equals

1] n-m+1 : m 2] n-m+1 : n 3] m : n-m+1 4] n : n-m+1

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.

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.

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.

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?

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

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

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

the maximum sum of the series 20,58/3,56/3,... is

(a)310

(b)290

(c)320

(d) none of these

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).

And one more question:

The arithmetic mean between two distinct positive numbers is twice the geometric mean between them.Find the ratio of greater to smaller.

Ans (2+?3):(2-?3)

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 }= 2Apth 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 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.....!!

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}sum to n terms

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

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

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

In an increasing G.P the sum of the first and last term is 66,the product of the second and the last but one is 128 and the sum of the terms is 126.How many terms are there in the progression?

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.

find the number of common terms in the sequence 3,7,11,......,407 and 2,9,16,......,709

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

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

if the sum of the 20th terms of G.P. is 244 times of sum of 10th term of G.P. then find the common ratio ?...plz answer

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 ??

Find the 20

^{th}term in the following sequence whosen^{th}term is