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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+a_{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 = ?Find 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.

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...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?Ans given: 25th term

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

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

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.

?, 20, 36, 68, 132, 260

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.

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

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.

Sum: a+b/2,a,3a-b/2,.... to 21 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

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

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 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.Q. Find the sum of n terms of the sequence.

7, 7.7, 7.77, 7.777, ......

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

the sum of the series 24,3,8,1,3,7...to 8 term is

a) 36

b) 36 [13/30]

c) 36 1/9

d) none of these .

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.

Find the sum of the series 2+11+101+1001+… to n terms.

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

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

4,8,16,13,7,14,__,___

a)8,16

b)9,18

c)5,10

d)18,16

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}find the sum of the following series 9+16+29+54+103+.........upto 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.

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

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}=?^{th}term and sum of the series:3+18+57+132+255.........

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

Find the sum of indicated number of terms .7,.07,.007,......;100 terms

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

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

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

2. SUM 1 + 3/4+7/16+15/64+31/256+.....TO INFINITY

SUM 1+2/2+3/2^2+4/2^3+.......TO N TERMS

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.

In an A.P.,s

_{3}=6,s_{6}=3,prove that 2(2n+1)S_{n}_{+4}=(n+4)S_{2n+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.

Experts !!

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

prove that the sum to n terms of the series 11+103+1005+.......... is 10 / 9 (10to the power n - 1)+n (sq).

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 1/a

^{2},1/b^{2},1/c^{2}are in H.P. ,then prove that (b+c),(c+a),(a+b) are also in H.P.if x1,x2,x3 ....xn are in H.P then prove that x1x2+x2x3+x3x4+....+xn-1xn =( n-1)x1xn

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.

^{2}=(2p-q) (2q-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 }= 2AQuestion 31. What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?

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).

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 5th term in the expansion of (3x+2) to the power 7

Ans given: a = 5.8, b = 4.4

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

^{2}-b^{2}] ,[b^{2}-c^{2}],[c^{2}-d^{2}]are in aplet 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.

Q. If Geometric mean b/w a & b is n times its harmonic mean then the value of a : 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

Q7. Find the sum of the positive terms of the arithmetic sequence 85, 78, 71,........

Q11. How many terms of the arithmetic sequence {1, 3, 5, , 7,......} will give a sum of 961?

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.

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

sum to n terms,50 terms of the series ... :7+7.7+7.77+7.777+.........?

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 (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 ??