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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 +..........

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}

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

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?Evaluate 3. 3

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

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

( answer = 1024 )

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

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.

For what values of k,the numbers ... 1+k,5/6 + k,13/18 + k are in G.P.

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

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

^{th}mean: n^{th}mean is 11:24, then find 'n'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

(xbe the A.M between x and y, then find the value of p.^{p}+ y^{p})/ (x^{p-1}+ y^{p-1})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.

find the sum of first 24 term of the A.P., if a1+a5+a10+a15+20+a25=225

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

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?

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

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

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

Find two numbers whose difference is 2 and whose AM exceeds the GM by 1/2.Âlet x=1+a+a2+.............. y=1+b+b2+.......... thn prove that

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

Q4 A person purchases a television set for Rs 16000. Its life is estimated to be 20 years. If the yearly depreciation is assumed to be constant, find the rate of depreciation and the price after 8 years.

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}^{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.

pls answer-- in an AP if a

_{p+1}= 2a_{q+1 }prove that a_{3p+1}= 2a_{p+q+1..}Find the sum to

nterms of the sequence, 6, 66, 666, 6666…-17.a1, a2 ,a3, a4, a5, a6, a7,a8, a9, a10,27a= -17

how a12 = 27 ???plzz answer this question as soon as possible.....

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

Find the sum to n terms of the sequence 1,-1,1,-1,.........,(-1)

^{n+1}If in an A.P., S

_{n}= n^{2}p and S_{m}=m^{2}p, then S_{p}=?1+(1+2)+(1+2+3)+(1+2+3+4)... find the sum of the series

What is the next number of the given series:-

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

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

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?

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.

If the roots of the cubic equation ax

^{3}+ bx^{2}+ cx + d = 0 are in G.P., then..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.

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

in an increasing GP , the sum of the first and the last term is 66 , the product of the second and the last but one term is 128 , and the sum of all the terms is 126. how many terms are there in the progression.

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

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

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.

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.

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 }= 2AQ).Find the sum of 500AM's between 2 and 3.

Q). Find the number of terms in the expansion of (1+3x +3x

^{2}+ x^{3})^{5}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 sum of 30th term of the sequence 7, 7.7, 7.77, 7.777..................

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

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

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.....!!

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

solve the equation 2+5+8...+x=155

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 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.

a1=3, an=3an-1 +2 for all n>1

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 ??