Sequence and Series questions
1035 published questions with worked solutions.
- Let a_1,a_2,a_3, be an A.P. If _ r=1 ^ a_r 2^r =4, then 4a_2 is equal to
- Different A.P.'s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the...
- If 1 2 3 4 + 1 3 4 5 + 1 4 5 6 + + 1 100 101 102 = k 101 , then 34k is equal to
- The 4^ th term of a G.P. is 500 and its common ratio is 1m, m N. Let S_n denote the sum of the first n terms of this G.P. If...
- Let a_1,a_2,a_3, be a G.P. of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and...
- Let a_1,a_2, ,a_n be in A.P. If a_5=2a_7 and a_ 11 =18, then 12 ( 1 a_ 10 + a_ 11 + 1 a_ 11 + a_ 12 + + 1 a_ 17 + a_ 18 ) is...
- The sum of the common terms of the following three arithmetic progressions 3,7,11,15, ,399; 2,5,8,11, ,359 and 2,7,12,17, ,197,...
- The 8^ th common term of the series S_1=3+7+11+15+19+ and S_2=1+6+11+16+21+ is
- The sum 1^2-2 3^2+3 5^2-4 7^2+5 9^2- +15 29^2 is
- If _3 2, _3(2^x-5), _3 (2^x- 7 2 ) are in an arithmetic progression, then the value of x is equal to _____.
- If ( 9 ), x, ( 7 18 ) are in arithmetic progression and ( 9 ), y, ( 5 18 ) are also in arithmetic progression, then |x – 2y| is...
- If for x, y P, x > 0, y= _ 10 x+ _ 10 x^ 1/3 + _ 10 x^ 1/9 + upto terms and 2+4+6+ +2y 3+6+9 .3y = 4 _ 10 x , then the ordered...
- The sum of 10 terms of the series 3 1^2 2^2 + 5 2^2 3^2 + 7 3^2 4^2 + is :
- Three numbers are in an increasing geometric progression with common ratio r. If the middle number is doubled, then the new...
- A function f(x) is given by f(x)= 5^x 5^x+5 , then the sum of the series f ( 1 20 )+f ( 2 20 )+f ( 3 20 )+ f ( 39 20 ) is equal...
- If [x] denote the greatest integer less than or equal to x,then _ n=8 ^ 100 [ (-1)^n.n 2 ] is equal to :
- Let S_n be the sum of the first n terms of an arithmetic progression. If S_ 3n =3S_ 2n , then the value of S_ 4n S_ 2n is :
- Let a_1, a_2, ...., a_ 10 be an AP with common difference –3 and b_1, b_2, ...., b_ 10 be a GP with common ratio 2. Let...
- If the sum of an infinite GP a, ar, ar^2, .... is 15 and the sum of the squares of its each term is 150, then the sum of ar^2,...
- If the arithmetic mean and geometric mean of the p^ th and q^ th terms of the sequence –16, 8, –4, 2, ... satisfy the equation...
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