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

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

if p arithmetic means are inserted between a and b, prove that d=b-a/p+1

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

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

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 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)

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

( answer = 1024 )

If a+b+...+l is a GP, prove that its sum is bl-a^2/b-a

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

if AM between two numbers exceeds their GM by 2 and the ratio of two numbers is 4, find the numbersif (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 (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!!

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.

_{c}a, log_{b}c, log_{a}b are in A.P. then find the common difference of the A.P.The sum of 11 terms of an AP whose middle term s 30 is

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

If

a,b,care in AP, prove thata.^{3}+ 4b^{3}+ c^{3}= 3b ( a^{2}+ c^{2})Sum the series: 1+3+7+15+31+............to n terms.

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.

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

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 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) .

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

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

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.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

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?

show that in an infinite gp each terms bears a constant ratio to the sum of all the terms that follow it.

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

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 a,b,c are in A.P. and a,b,d are in G.P. ,prove that a,a-b,d-c are in G.P.

1+2x+3x

sum of this series^{2}+4x^{3}..........to infinityIf 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}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???????

^{b-c})x (Y^{c-a}) x(Z^{a-b})=1_{p+q}=m and t_{p-q}=n. Then find t_{p}.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?

Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 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.

Find the sum to

nterms of the sequence, 6, 66, 666, 6666…^{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=cIf in an A.P., S

_{n}= n^{2}p and S_{m}=m^{2}p, then S_{p}=?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},..........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 the pth qth and rth terms of a GP be x, y, z respectively prove that x

^{q-r}. y^{r-p}. z^{p-q}=11+(1+2)+(1+2+3)+(1+2+3+4)... find the sum of the series

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

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

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

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

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 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}

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

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

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.

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

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.

The sum of four distinct numbers in G.P is 60 and the arithmetic mean of the first and the last is 18. 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 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?

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 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}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.....

sum the following series to n terms

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

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

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

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

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

The sum of the first n terms of the series:

1/2 + 3/4 + 7/8 + 15/16 + ....... is?

Please help me in working out this problem.

Find the sum of sequence, 7, 77, 777, 7777..... to n terms ???

plz ans fast....

its very urgent

Find the sum of n terms of the series the rth term of which is (2r+1)2^r

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

Between 1 and 31,

mnumbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7^{th}and (m– 1)^{th}numbers is 5:9. Find the value ofm.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 ??