CAT 1993 — QA Question 23
Geometric ProgressionEasy
Let Un+1 = 2Un + 1 (n = 0, 1, 2, ...) and u0 = 0. Then u10 is nearest to
Answer & solution
Correct answer: 1023
1023
- B
2047
- C
4095
- D
8195
Solution
U0 = 0 = 20 – 1 = 0
U1 = 2 × 0 + 1 = 1 = 21 – 1
U2 = 2 × 1 + 1 = 3 = 22 – 1
U3 = 2 × 3 + 1 = 7 = 23 – 1 and so on.
⇒ Un = 2n - 1
∴ U10 = 210 – 1 = 1023.
Hence, option (a).