Question

What are the first four terms of the sequence modeled by the recursive formula aⁿ=aⁿ-1⁵, when a¹=-3?

Answer 1

The first four terms of the sequence modeled by the recursive formula aⁿ=aⁿ-1⁵, when a¹=-3, are -3, -243, -243, -243.

Step-by-step explanation:

The recursive formula given is aⁿ=aⁿ-1⁵, with an initial value of a¹=-3. To find the first four terms of the sequence, we can use the recursive formula to generate each term. Starting with a¹=-3, we can substitute the value of n into the formula to calculate the next term. Let's calculate the values step by step:

1. First term: a¹ = -3
2. Second term: a² = a¹⁵ = (-3)⁵ = -243
3. Third term: a³ = a²⁵ = (-243)⁵ = -243, hence the third term is the same as the second term.
4. Fourth term: a⁴ = a³⁵ = (-243)⁵ = -243, hence the fourth term is the same as the third term.

Therefore, the first four terms of the sequence are: -3, -243, -243, -243.