Sequence and Series questions
1035 published questions with worked solutions.
- If x, y, z are in GP, then which of the following is/are correct? 1. (3x), (3y), (3z) are in AP 2. xyz+ (x), xyz+ (y), xyz+ (z)...
- If _ 10 2, _ 10 (2^x-1), _ 10 (2^x+3) are in AP, then what is x equal to?
- If 1 b+c , 1 c+a , 1 a+b are in HP, then which of the following is/are correct? 1. a, b, c are in AP 2. (b+c)^2, (c+a)^2, (a+b)^2...
- If C(n, 4), C(n, 5) and C(n, 6) are in AP, then what is the value of n?
- Let S_k denote the sum of first k terms of an AP. What is S_ 30 S_ 20 -S_ 10 equal to?
- Let m be the minimum possible value of _3(3^ y_1 + 3^ y_2 + 3^ y_3 ), where y_1, y_2, y_3 are real numbers for which y_1 + y_2 +...
- Let a_1, a_2, a_3, be a sequence of positive integers in arithmetic progression with common difference 2. Also, let b_1, b_2,...
- Let l_1, l_2, , l_ 100 be consecutive terms of an arithmetic progression with common difference d_1, and let w_1, w_2, , w_ 100...
- Let a_1, a_2, a_3, be an arithmetic progression with a_1 = 7 and common difference 8. Let T_1, T_2, T_3, be such that T_1 = 3 and...
- Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5. Let the sum of its first five terms be...
- Suppose a_ 1 , a_ 2 , ... a_ n , ... be an arithmetic progression of natural numbers. If the ratio of the sum of first five terms...
- If a_ 1 , a_ 2 , a_ 3 _____ and b_ 1 , b_ 2 , b_ 3 _____ are A.P., and a_ 1 = 2, a_ 10 = 3, a_ 1 b_ 1 = 1 = a_ 10 b_ 10 , then a_...
- If x = _ n=0 ^ a^ n , y = _ n=0 ^ b^ n , z = _ n=0 ^ c^ n , where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc 0, then :
- If the sum of the first ten terms of the series 1/5 + 2/65 + 3/325 + 4/1025 + 5/2501 + ... is m/n, where m and n are co-prime...
- If 6/3^ 12 + 10/3^ 11 + 20/3^ 10 + 40/3^ 9 + … + 10240/3 = 2^ n m, where m is odd, then m·n is equal to _____.
- Let , and be three positive real numbers. Let f(x) = x^ 5 + x^ 3 + x, x R and g : R R be such that g(f(x)) = x for all x R. If a_...
- Consider the sequence a_ 1 , a_ 2 , a_ 3 , … such that a_ 1 = 1, a_ 2 = 2 and a_ n+2 = 2/a_ n+1 + a_ n for n = 1, 2, 3, …. If (a_...
- Let x_ 1 , x_ 2 , x_ 3 , …, x_ 20 be in geometric progression with x_ 1 = 3 and the common ratio 1/2. A new data is construction...
- If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 and a + n =...
- Let for n = 1, 2, …, 50, S_ n be the sum of the infinite geometric progression whose first term is n^ 2 and whose common ratio is...
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