Question

Find the third, fourth, and fifth terms of the sequence defined by:

a₁ = 5,
a₂ = 8,
and
aₙ = 2aₙ₋₁ − aₙ₋₂ for n ≥ 3.

a₃ =
a) 11
b) 18
c) 21
d) 26

a₄ =
a) 31
b) 43
c) 50
d) 57

a₅ =
a) 69
b) 92
c) 105
d) 122

Answer 1

The third, fourth, and fifth terms of the given recursive sequence are 11, 14, and 17, respectively. It appears there may be an error in the provided options for the fourth and fifth terms.

Step-by-step explanation:

To find the third, fourth, and fifth terms of the sequence where a₁ = 5, a₂ = 8, and the recursive formula is aₙ = 2aₙ₋₁ - aₙ₋₂ for n ≥ 3, we need to apply the recursive formula sequentially to get each subsequent term.

• To find a₃, we use the formula to get a₃ = 2 * a₂ - a₁ = 2 * 8 - 5 = 16 - 5 = 11.
• Next, for a₄, we apply the formula again: a₄ = 2 * a₃ - a₂ = 2 * 11 - 8 = 22 - 8 = 14.
• Lastly, to find a₅, we use the values of a₃ and a₄: a₅ = 2 * a₄ - a₃ = 2 * 14 - 11 = 28 - 11 = 17.

So, the third term is 11 (option a), the fourth term is 14 (not listed in the options provided), and the fifth term is 17 (not listed in the options).