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?

1 Answer
Y
May 13, 2017

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

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