Find the first 5 terms of the sequence with
a1=6 and an=2a n-1 -1 for n _>2
a. 6, 12, 24, 48, 96
b. 6, 11, 21, 41, 81
c. 6, 7, 8, 9, 10
d. 1, 2, 3, 4, 5
To find the first 5 terms of the given sequence, we can use the recursive formula. The recursive formula for the sequence is given as aₙ = 2aₙ₋₁ - 1.
Given that a₁ = 6, we can use this information to find the next terms of the sequence.
To find a₂, we substitute n = 2 into the formula:
a₂ = 2a₂₋₁ - 1
= 2a₁ - 1
= 2(6) - 1
= 12 - 1
= 11
To find a₃, we substitute n = 3 into the formula:
a₃ = 2a₃₋₁ - 1
= 2a₂ - 1
= 2(11) - 1
= 22 - 1
= 21
To find a₄, we substitute n = 4 into the formula:
a₄ = 2a₄₋₁ - 1
= 2a₃ - 1
= 2(21) - 1
= 42 - 1
= 41
To find a₅, we substitute n = 5 into the formula:
a₅ = 2a₅₋₁ - 1
= 2a₄ - 1
= 2(41) - 1
= 82 - 1
= 81
Therefore, the first 5 terms of the sequence are 6, 11, 21, 41, 81.
Hence, the correct answer is option b. 6, 11, 21, 41, 81.