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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