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=(- 1)^n
Practice makes perfect
Explicit equations for geometric sequence 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= - 1. Let's observe the other terms to determine the common ratio r.
- 1* (- 1) →1* (- 1) →- 1* (- 1) →1...
By substituting these two values into the explicit equation and simplifying, we can find the formula for this sequence.
