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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 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.

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

What is the next number of the given series:-

4,10,34,94,214,424...

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

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

(a)310

(b)290

(c)320

(d) none of these

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?In the A.P. whose common difference is non-zero, the sum of first 3n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2n terms to the nwxt 2n terms is how much?

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

-3/4,3/16,-3/64

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

( answer = 1024 )

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

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

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

(A)15 (B)48 (C)44 (D)42

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) .

?, 20, 36, 68, 132, 260

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

In an A.P.,s

_{3}=6,s_{6}=3,prove that 2(2n+1)S_{n}_{+4}=(n+4)S_{2n+1}.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.For what values of k,the numbers ... 1+k,5/6 + k,13/18 + k are in G.P.

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?

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.

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.

$2.Ifxyz=\left(1-x\right)\left(1-y\right)\left(1-z\right)where0\le x,y,z\le 1,thentheminimumvalueofx\left(1-z\right)+y\left(1-x\right)+z\left(1-y\right)is:\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(a\right)\frac{3}{2}\left(b\right)\frac{1}{4}\left(c\right)\frac{3}{4}\left(d\right)\frac{1}{2}$

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

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

An A.P consists of 12 terms whose sum is 354. The ratio of the sum of the even terms to the sum of the odd terms is 32:27. Find the common difference of the progression.

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}19. Consider a three digit number x

_{1}x_{2}x_{3}such that x_{1}.x_{2}.x_{3}$\in $ N. Then the number of positive integral solutions of x_{1}.x_{2}.x_{3 }= 480 is ${\lambda}^{2}$ -100, then the sum of the digits of $\left|\lambda \right|$ is(A) 8 (B) 9 (C) 7 (D) 10

^{b-c})x (Y^{c-a}) x(Z^{a-b})=1_{p+q}=m and t_{p-q}=n. Then find t_{p}.Q.17. Sonia has 55 blocks. She decides to to stack up all the blocks so that each row has one less block than below. She wants to end up with just 1 block on top. How many should she put in the bottom row?

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…7^2+9^2+11^2+............n terms

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}=?i. 1.3+2.5+3.7+....+n(2n+1)

ii. .9+.99+.999+.....to n-term.

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

Find the sum of the sequence 0.4, 0.44, 0.444â€¦â€¦. up to

nterms.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.

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

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 the first three terms of a G.P. is to the sum of first six terms as 125:152.Find the common ratio of the G.P.

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,c are in a.p and x,y,z are in g.p. then prove that x^b-c x y ^c-a x z^a-b = 1 descriptive form???????

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

(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 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.

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.

Let

candbbe the roots of x^{2}-6x-2=0 (cb). Ifa

_{n}=c^{n}-b^{n}where (n=1)then a

_{10}-2a_{8}/2a_{9}=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.....

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

Ans given: a = 5.8, b = 4.4

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 the sum of the 3 terms of a G.P is 21 and sum of their squares is 189 find the three no.s in G.P.

how to find the solution.. pls help.....

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

THE THIRD TERM OF A G.P IS 2/3 & THE 6TH TRERM IS 2/81 FIND THE 8TH TERM

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 3 numbers in AP whose sum is 24 and sum oftheir cubes is 1968.

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 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

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 ??

100

Sigma 3

^{r}(2-2r)/(r+1)(r+2)r=2

Options : -

(A) 1/2 - {3

^{100}/100(101)}(B) 3/2 - {3

^{101}/101(102)}