Question

A sequence can be generated using an + 1 = –0.25 + an, where a1 = 5 and n is a whole number greater than 1. What are the first 5 terms in the sequence?

Answer 1

To find the first 5 terms in the sequence, we can apply the given recursive formula.

a1 = 5

Applying the formula for a2:
a2 = -0.25 + a1 = -0.25 + 5 = 4.75

Applying the formula for a3:
a3 = -0.25 + a2 = -0.25 + 4.75 = 4.5

Applying the formula for a4:
a4 = -0.25 + a3 = -0.25 + 4.5 = 4.25

Applying the formula for a5:
a5 = -0.25 + a4 = -0.25 + 4.25 = 4

Therefore, the first 5 terms in the sequence are 5, 4.75, 4.5, 4.25, and 4.