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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 of n terms of the sequence

( x + 1/x )

^{2}, ( x^{2}+1 /x^{2})^{2}, (x^{3}+ 1/x^{3})^{2},..........Find the sum to n terms of the series :- 5 + 11 + 19 + 29 + 41 +..........

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

Sum of first n the terms in the following series Cot-7 + cot-13 + cot-3 + cot-21 + ........... is given by:

(1) tan

^{-1}(n/n+2) (2) Cot^{-1}(n+2/n) (3) tan^{-1 }(n+1) - Tan^{-1}1 (4) all of thesea 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 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 a, b, c respectively, prove that

a^(q-r).b^(r-p).c^(p-q)=1;

where ^=raised to the power

If the sum of n terms of an A.P. is 2mn + pn

^{2}, where m and p are constants, find the common differenceThe third term of a GP is 4 , find the product of its first five terms .

( answer = 1024 )

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

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

The number 1111.....1(91 times) is a

A) prime b) non prime c) even

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.

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

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.

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

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

the sum of (3/1?2) (1/2)+(4/2?3) (1/2)?+ (5/3?4) (1/2)?.... to n terms is

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) .

If a is the A.M between b and c and g1, g2 are two geometric means between b and c. show that g13+g23=2abc.

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

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

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.If S

_{r}denotes the sum of r terms of an A.P. and S_{a}/a^{2}= S_{b}/b^{2}= c . Then S_{c}is(A) c

^{3}(B) c/ab (C) abc (D) a+b+c . Give the process also .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

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

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)

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}^{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…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}

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

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

What is non constant A.P.

?

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.

Find the sum of the sequence 0.4, 0.44, 0.444……. up to

nterms.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.

Q6. Second , 31st and the last terms of an AP are 31/4, 1/2 and -13/2 respectively. Find the number of terms in the AP.

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.

Insert 10 A.M's between 5 -17 prove that their sum is 10 times the A.M between them.

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

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.

The sum of three numbers in G.P. is 14. If the first two terms are each increased by 1 and the third term decreased by 1, the resulting numbers are in A.P. Find the numbers.

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 A = 1+r

^{a}+r^{2a}+r^{3a}+ ..... infinity and B = 1 +r^{b}+r^{2b}+ r^{3b}+ ..... infinity, then find a/b (where |r|<1).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}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!!

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

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

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.....!!

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

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 of the series 3+5+7+6+9+12+13+17+...3n terms

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 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

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 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 ??