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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 +..........

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.

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

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}

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 )

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

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

Q 9

9. Sum up 3+5+11+29.........to n terms.

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.

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?

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

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

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

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)

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) .

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.

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,dare in G.P, prove that are in G.P.find the sum of the following series to n terms: (i) 3+5+9+15+23_ _ _

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

if the sum of n terms of a progression be a quadratic expression in n show that it is an AP

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.

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

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}What is non constant A.P.

?

^{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…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 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}=?sum of series 1.2^2 + 3.3^2 + ..................n terms

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

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

that their 6th term are equal.

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

Find the sum the following series to n terms:

3+7+14+24+37+.........

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.

sum the following series to n terms

1+4+13+40+121+.......

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.

_{c}a, log_{b}c, log_{a}b are in A.P. then find the common difference of the 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.

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

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

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 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

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

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).

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.

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 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.....!!

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,c, and d are in GP, show that

(b-c)^2 + (c-a)^2 + (d-b)^2 = (a-d)^2

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

1. The value of auto rickshaw gets depreciated by 20% per year. what would be its estimated value at the end of 5 years if the present value is Rs. 24000.

2. Find the nth term of 0.4, 0.44, 0.444, .......

3. The monthly salary of a person was Rs. 320 fro each of the first three years. He got annual increment of Rs. 40 per month for each of the following successive 12 years. his salary remained stationary till retirement when he found that his average monthly salary during his service period was Rs. 698. Find the period of service

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

3^(1/2).3^(1/4).3^(1/8)....=3

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

Que. Find the sum to n terms:

1/1.3.5 +1/3.5.7 +1/5.7.9 +.......

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

The sum of series 1/2! + 1/4! + 1/6! + ..... isFind 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 (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 ??