Question

How do you write the first five terms of the geometric sequence `a_1=7, a_(k+1)=2a_k` and determine the common ratio and write the nth term of the sequence as a function of n?

Answer 1

Common Ratio: `2`
Explicit formula: `a_n=7(2^(n-1))`

Explanation:

Given the first term, `a_1=7` and the recursive formula for the geometric sequence, `a_(k+1)=2a_k`, we know the common ratio must be `2`, since the recursive formula multiplies `2` to the `k^(th)` term to get the `(k+1)^(th)` term.

Since we know the common ratio is `2` and the first term is `7`, we can write our explicit formula for the geometric sequence using the general form:
`a_n=a_1(r^(n-1))`

By substituting our known values, we get:
`a_n=7(2^(n-1))` which allows us to find the nth term as a function of n