What is the first term of the sequence? What is the common ratio between terms? Use these values in the explicit equation for geometric sequences.
2187/8
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= 18. Let's observe the other terms to determine the common ratio r.
1/8* 3 →3/8* 3 →9/8...
By substituting these two values into the explicit equation and simplifying, we can find the formula for this sequence.
a_n=a_1r^(n-1) ⇒ a_n= 1/8( 3)^(n-1)
This equation can be used to find any term in the given sequence. To find a_8, the eighth term in the sequence, we substitute 8 for n.
