Answer:
The first five terms are 6, 11, 21, 41, 81 ⇒ D
Explanation:
∵ The rule of the sequence is a(1) = 6; a(n) = 2 a(n - 1) - 1 for n ≥ 2
∴ The first term of the sequence is 6
∴ The value of n represents the position of the term
∵ n = 2
∴ a (n - 1) = a(2 - 1) = a1
∵ a1 = 6
→ Substitute a1 by 6
∴ a(2) = 2(6) - 1 = 12 - 1
∴ a(2) = 11
∵ n = 3
∴ a (n - 1) = a(3 - 1) = a2
∵ a2 = 11
→ Substitute a2 by 11
∴ a(3) = 2(11) - 1 = 22 - 1
∴ a(3) = 21
∵ n = 4
∴ a (n - 1) = a(4 - 1) = a3
∵ a3 = 21
→ Substitute a3 by 21
∴ a(4) = 2(21) - 1 = 42 - 1
∴ a(4) = 41
∵ n = 5
∴ a (n - 1) = a(5 - 1) = a4
∵ a4 = 41
→ Substitute a4 by 41
∴ a(5) = 2(41) - 1 = 82 - 1
∴ a(5) = 81
∴ The first five terms are 6, 11, 21, 41, 81