Question

I will give brainliest to whoever answers it correctly
An arithmetic sequence is represented by the explicit formula A(n) = 8 - 6(n - 1) What is the recursive formula? Group of answer choices

Answer 1

Answer:

• A(1) = -4
• A(n) = A(n - 1) - 6

Step-by-step explanation:

Given

• AP with the explicit formula A(n) = 8 - 6(n - 1)

To find

• Recursive formula

Solution

Recursive formula is the formula A(n) = A(n - 1) + d

Based on the explicit formula we have:

• A(n) = 8 - 6(n - 1) = 8 - 6n + 6 = 2 - 6n
• A(n - 1) = 2 - 6( n - 1) = 2 - 6n + 6 = 8 - 6n

The common difference is:

• d  = A(n) - A(n - 1) = 2 - 6n - (8 - 6n) = 2 - 6n - 8 + 6n = - 6

The first term is:

• A(1) = 2 - 6(1) = 2 - 6 = -4

So the recursive formula is:

• A(1) = -4
• A(n) = A(n - 1) - 6