Question

Consider the arithmetic sequence defined recursively by the function H (n) = 2 • H (n - 1) with an initial term H (1) = 8. What is the 7th term of this sequence?

Answer 1

To find the 7th term of the arithmetic sequence defined by H(n) = 2 • H(n - 1) and H(1) = 8, the recursive formula is applied six times, resulting in the 7th term being 512.

Step-by-step explanation:

The question asks for the 7th term of the arithmetic sequence defined by a recursive function H(n) = 2 • H(n - 1), with the initial term H(1) = 8. To find the 7th term, we need to apply the recursive formula successively starting from the initial term.

1. H(2) = 2 • H(1) = 2 • 8 = 16
2. H(3) = 2 • H(2) = 2 • 16 = 32
3. H(4) = 2 • H(3) = 2 • 32 = 64
4. H(5) = 2 • H(4) = 2 • 64 = 128
5. H(6) = 2 • H(5) = 2 • 128 = 256
6. H(7) = 2 • H(6) = 2 • 256 = 512

Therefore, the 7th term of the sequence is 512.