Sequence & Series Level-3 Quiz-2

1. Given A = 2⁶⁵ and B = (2⁶⁴ + 2⁶³ + 2⁶² + … + 2⁰), which of the following is true?

2. Sum of first 12 terms of a GP is equal to the sum of the first 14 terms in the same GP. Sum of the first 17 terms is 92, what is the third term in the GP?

3. The nth term (tn) of a certain sequence is defined as tn = tn-1 + 4. If t1 = -7 then find out value of t71.

4. The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + …+ 95 x 99 is?

5. If log 2, log (2x – 1) and log (2x + 3) are in A.P, then x is equal to?

6. Let the m th and n th terms of a Geometric progression be 3/4 and 12, respectively, when m < n. If the common ratio of the progression is an integer r, then the smallest possible value of r + n – m is?

7. A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of 5 children. How many toffees were there in his stock initially?

8. Sum of first 25 terms in AP is 525, sum of the next 25 terms is 725, what is the common difference?

9.

Consider a, b, c in a G.P. such that |a + b + c| = 15. The median of these three terms is a, and b = 10. If a > c, what is the product of the first 4 terms of this G.P.?

10. Let the n^th term of AP be defined as t_n, and sum up to ‘n’ terms be defined as S_n. If |t₈| = |t₁₆| and t₃ is not equal to t₇, what is S₂₃?