Question

Create an explicit formula of the sequence. 7, 14, 28, 56, ..., Find the 10th term of the sequence. Complete your work in the space provided or upload a file that can display math symbols if your work requires it. In your answer, be sure to include the explicit formula and the 10th term of the sequence.

Answer 1

an = 7·2^(n-1)

a10 = 3584

Explanation:

(a) The terms of the sequence do not have a common difference, but they do have a common ratio. That ratio is 14/7 = 2. The general term of a geometric sequence with first term a1 and common ratio r is ...

an = a1·r^(n-1)

For a1=7 and r=2, the explicit formula is ...

an = 7·2^(n-1)

__

(b) The 10th term is ...

a10 = 7·2^(10 -1) = 7·512

a10 = 3584