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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+aA) 0

B) 2

C) 5

D) 9

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

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

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

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

( answer = 1024 )

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?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 n terms of the sequence

( x + 1/x )

^{2}, ( x^{2}+1 /x^{2})^{2}, (x^{3}+ 1/x^{3})^{2},..........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.

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

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

find method to find out value of x if value of x is 62

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

The sum of three numbers which are consecutive terms of an A.P. is 21.If the second number is reduced by 1 while third number is increased by 1,three consecutive terms of a G.P. result.Find numbers.

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

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

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 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

a,b,c,dare in G.P, prove that are in G.P.prove that:2^1/4 . 4^1/8 . 8^1/16............upto infinity=2

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

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

the sum of n terms oof two ap are in the ratio(7n-5) :(5n+17).Show

that their 6th term are equal.

^{b-c})x (Y^{c-a}) x(Z^{a-b})=1_{p+q}=m and t_{p-q}=n. Then find t_{p}.show that in an infinite gp each terms bears a constant ratio to the sum of all the terms that follow it.

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

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

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

if p arithmetic means are inserted between a and b, prove that d=b-a/p+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}given that n arithmetic means are inserted between two sets of numbers a, 2b and 2a, b where a, b are real numbers . suppose further that mth mean between these two sets of numbers is same then the ratio a : b equals

1] n-m+1 : m 2] n-m+1 : n 3] m : n-m+1 4] n : n-m+1

Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.

The sides of a right angled triangle are in ap show that the sides are in the ratio 3:4:5 ?

Please reply soooooooooooooooooooooon

Find the sum to

nterms of the sequence, 6, 66, 666, 6666…7^2+9^2+11^2+............n terms

If in an A.P., S

_{n}= n^{2}p and S_{m}=m^{2}p, then S_{p}=?Urgent!! If the sum of first n nos. of AP is cn

^{2}then, the sum of the squares of these n terms is..FIND FOUR NUMBERS IN AP WHOSE SUM IS 20 &SUM OF WHOSE SQUARES IS 120

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.

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

pls answer-- in an AP if a

_{p+1}= 2a_{q+1 }prove that a_{3p+1}= 2a_{p+q+1..}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

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 the following series to n terms:

3+7+14+24+37+.........

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.

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.

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

Barranges to payoff a debt of Rs.4,800 in 24 monthly instalments which form an A.P. After 20 instalmentsBbecomesIf a+b+...+l is a GP, prove that its sum is bl-a^2/b-a

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 abc are in gp show that

^{a2 b2c2}^{ ALSO IN GP}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 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

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.

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).

Four different integers from an increasing A.P .one of these numbers is equal to the sum of the squares of the other three numbers. 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 }= 2ASum of an infinite GP is 5/4 times the sum of all odd terms. The comon ratio of the GP is?

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

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.

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

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.....

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

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

The largest term common to the sequence 1,11,21,31,.... to 100 terms and 31,36,41,46,..... to 100 terms is (A) 381 (B) 471 (C) 281 (D) none . Please give the solution alse.

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

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

^{2}+ b^{2}, ab+ bc, b^{2}+ c^{2}are also in GPFind the sum of sequence, 7, 77, 777, 7777..... to n terms ???

plz ans fast....

its very urgent

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.

if a, b are the roots of x^2 - 3x + p =0 and c, d are the roots of x^2 - 12x +q = 0 where a,b,c,d form a G.P, find the ratio of (q+p):(q-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.....!!

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

If pth,qth,rth and sth terms of an A.P. are in G.P.,then show that (p-q),(q-r),(r-s) are also in G.P.(example of ncert).

plzzz explain it couldn't understand !!

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

If a,b,c are in AP as well as in GP then show that a=b=c.

If n A.M.s are inserted between two numbers,prove that the sum of the means equidistant from the beginning and the end is constant.