Which one of the given options is a possible value of z in the following sequence? 3, 7, 15, z, 63, 127, 255 A. 30 B. 40 C. 15 D. 31

GATE 2024 · General Aptitude · Sequence Series · medium

Answer: z = 31

1. Express each known term as 2^n - 1: a_1=3=2^2-1, a_2=7=2^3-1, a_3=15=2^4-1, a_5=63=2^6-1, a_6=127=2^7-1, a_7=255=2^8-1.
2. Find z = a_4: For k=4: a_4 = 2^(4+1) - 1 = 2^5 - 1 = 32 - 1 = 31.
3. Verify using the doubling rule: 2*15+1=31 (confirms z=31). Then 2*31+1=63 (matches a_5=63). Fully consistent.