Question

write an equation to describe the sequence below. use n to represent the position of a term in the sequence, where n = 1 for the first term. 26.5, 79.5, 238.5, ... write your answer using decimals and integers. a_n = ( )^{n - 1}

Explanation:

Step1: Identify the first - term

The first term $a_1$ of the sequence is $26.5$, so when $n = 1$, $a_1=26.5$.

Step2: Find the common ratio

To find the common ratio $r$, divide the second - term by the first - term. $r=\frac{79.5}{26.5}=3$.

Step3: Write the general formula for a geometric sequence

The general formula for a geometric sequence is $a_n=a_1r^{n - 1}$. Substituting $a_1 = 26.5$ and $r = 3$ into the formula, we get $a_n=26.5\times3^{n - 1}$.

Answer:

$a_n = 26.5(3)^{n - 1}$