Sequence and Series questions
1035 published questions with worked solutions.
- Let S_k, k = 1, 2, , 100, denote the sum of the infinite geometric series whose first term is k-1 k! and the common ratio is 1 k...
- Let a_1, a_2, a_3, , a_ 11 be real numbers satisfying a_1 = 15, 27 - 2a_2 > 0 and a_k = 2a_ k-1 - a_ k-2 for k = 3, 4, , 11. If...
- Let a_1, a_2, a_3, , a_ 100 be an arithmetic progression with a_1 = 3 and S_p = _ i=1 ^ p a_i, 1 p 100. For any integer n with 1...
- Let a_1, a_2, a_3, be in harmonic progression with a_1 = 5 and a_ 20 = 25. The least positive integer n for which a_n < 0 is
- Let S_n = _ k=1 ^ 4n (-1)^ k(k+1) 2 k^2. Then S_n can take value(s)
- A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and the sum of the numbers...
- Let a, b, c be positive integers such that b a is an integer. If a, b, c are in geometric progression and the arithmetic mean of...
- Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum of the first seven...
- Let b_i>1 for i=1,2, ,101. Suppose _eb_1, _eb_2, , _eb_ 101 are in Arithmetic Progression (A.P.) with the common difference _e2....
- The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its...
- Let X be the set consisting of the first 2018 terms of the arithmetic progression 1,6,11, , and Y be the set consisting of the...
- Let AP(a;d) denote the set of all the terms of an infinite arithmetic progression with first term a and common difference d>0. If...
- How many geometric progressions is/are possible containing 27, 8 and 12 as three of its/their terms?
- What is the greatest value of the positive integer n satisfying the condition 1+ 1 2 + 1 4 + 1 8 + + 1 2^ n-1 <2- 1 1000 ?
- What is the sum of the series 0 3+0 33+0 333+ n terms?
- If the sum of m terms of an AP is n and the sum of n terms is m, then the sum of (m+n) terms is
- The fifth term of an AP of n terms, whose sum is n^2-2n, is
- The sum of the first n terms of the series 1 2 + 3 4 + 7 8 + 15 16 + is equal to
- Let x, y, z be positive real numbers such that x, y, z are in GP and ^ -1 x, ^ -1 y and ^ -1 z are in AP. Then which one of the...
- If S_n=nP+ n(n-1)Q 2 , where S_n denotes the sum of the first n terms of an AP, then the common difference is
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