Sequence and Series questions
1035 published questions with worked solutions.
- The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is 27 19 . Then the common...
- The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is:
- If a_1, a_2, a_3, are in A.P. such that a_1 + a_7 + a_ 16 = 40, then the sum of the first 15 terms of this A.P. is:
- If the sum of the first 40 terms of the series, 3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 +…… is (102)m, then m is equal to:
- Let a_1, a_2, a_3, be a G.P. such that a_1<0, a_1+a_2=4 and a_3+a_4=16. If _ i=1 ^ 9 a_i=4 , then is equal to:
- Let a_n be the n^ th term of a G.P. of positive terms. If _ n=1 ^ 100 a_ 2n+1 =200 and _ n=1 ^ 100 a_ 2n =100, then _ n=1 ^ 200...
- The number of terms common to the two A.P.'s 3, 7, 11, ….. 407 and 2, 9, 16, …. 709 is ___________.
- If the sum of the series 20+19 3 5 +19 1 5 +18 4 5 + upto n^ th term is 488 and the n^ th term is negative, then-
- If m arithmetic means (A. Ms) and three geometric means (G. Ms) are inserted between 3 and 243 such that 4^ th A.M. is equal to...
- Let S_n denote the sum of the first n terms of an arithmetic progression. If S_ 10 = 390 and the ratio of the tenth the fifth...
- If three successive terms of a G.P. with common ratio r (r > 1) are the lengths of the sides of a triangle and [r] denotes the...
- Let 3, a, b, c be in A.P. and 3, a − 1, b + 1, c + 9 be in G.P. Then, the arithmetic mean of a, b and c is:
- Let 3, 7, 11, 15, …, 403 and 2, 5, 8, 11, …, 404 be two arithmetic progressions. Then the sum of the common terms in them, is...
- Let three real numbers a, b, c be in arithmetic progression and a + 1, b, c + 3 be in geometric progression. If a > 10 and the...
- The value of 1 2^2 + 2 3^2 + + 100 (101)^2 1^2 2 + 2^2 3 + + 100^2 101 is
- Let the first three terms 2, p and q, with q ≠ 2, of a G.P. be respectively the 7th, 8th and 13th terms of an A.P. If the 5th...
- Let a_1, a_2, a_3, be in an arithmetic progeression of positive terms. Let A_k = a_1^2 - a_2^2 + a_3^2 - a_4^2 + + a_ 2k-1 ^2 -...
- For x ≥ 0, the least value of K, for which 4^ 1+x + 4^ 1-x , K2, 16^x + 16^ -x are three consecutive terms of an A.P. is equal to:
- If 1 + 3 - 2 2 3 + 5 - 2 6 18 + 9 3 - 11 2 36 3 + 49 - 20 6 180 + up to ∞ = 2 + ( ba + 1 ) _e ( ab ), where a and b are integers...
- The greatest positive integer k, for which 49^k+1 is a factor of the sum 49^ 125 +49^ 124 + +49^2+49+1, is :
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