Sequence and Series questions
1035 published questions with worked solutions.
- If a_1,a_2, ,a_ n+1 are in AP, then 1 a_1a_2 + 1 a_2a_3 + + 1 a_na_ n+1 is
- If A_1,A_2 are two A.M.'s between a and b and G_1,G_2 are two GM's between a and b then A_1+A_2 G_1G_2 is
- The sum to n terms of the series 2^2+4^2+6^2+ is
- Consider the following statements: 1. If a_n denotes the n^ th term of an AP, then a_n= a_ n+k +a_ n-k 2. 2. In an AP, if the sum...
- x+y+z=15, if 9,x,y,z,a are in AP, while 1x+ 1y+ 1z= 53, if 9,x,y,z,a are in HP, then value of a will be
- If the p^ th , q^ th and r^ th term of a GP and HP are a,b,c, then a(b-c) a+b(c-a) b+c(a-b) c is equal to
- If a,b,c,d,e,f are in AP, then the value of e-c will be
- The sum of the infinite terms of the series 5 3^2+7^2 + 9 7^2+11^2 + 13 11^2+15^2 + is
- The AM, HM and GM between two numbers are 144 15 , 15 and 12, but not necessarily in this order. Then, HM, GM and AM respectively...
- If the ratio of the sum of n term of two AP's be (7n+1):(4n+27), then the ratio of their 11^ th term will be
- Number of values of x for which [x], sgn x, x (x 0) are in AP, is
- If a_1,a_2,a_3, ,a_ 24 are in arithmetic progression, a_1+a_5+a_ 10 +a_ 15 +a_ 20 +a_ 24 =225, then a_1+a_2+a_3+ +a_ 23 +a_ 24 is...
- The n^ th term of the series 1^3 1+ 1^3+2^3 1+3 + 1^3+2^3+3^3 1+3+5 + will be
- If the sum of an infinite GP and the sum of square of its term is 3, then the common ratio of the first series is
- Let S_1,S_2, be squares such that for each n 1, the length of a side of S_n equals the length of a diagonal of S_ n+1 . If the...
- The sum of the series 1 2 3+2 3 4+3 4 5+ to n terms is
- The sum of the series 1 n+2 (n-1)+3 (n-2)+ +n 1 is
- If 2, (2^n-1 ) and (2^n+3 ) are in AP, then n is equal to
- The sum of the series 5.05+1.212+0.29088+ is
- Let T_r be the r^ th term of an AP for r=1,2,3, If for some positive integers m,n, we have T_m= 1n and T_n= 1m, then T_ mn equals
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