What is the first term of the sequence? What is the common ratio between terms? Use these values in the explicit equation for geometric sequence.
a_n=2(2)^(n-1)
Practice makes perfect
Explicit equations for geometric sequences follow a specific format.
a_n= a_1 r^(n-1)
In this form, a_1 is the first term in a given sequence, r is the common ratio from one term to the next, and a_n is the {\color{#FF0000}{n}}^\text{th} term in the sequence. For this exercise, the first term is a_1= 2. Let's observe the other terms to determine the common ratio r.
2* 2 →4* 2 →8 ...
We can see that the common ratio is r = 2. By substituting these two values into the explicit equation we can find the formula for this sequence.
a_n= 2( 2)^(n-1)
