Question

write an equation to describe the sequence below, and then find the 4th term. use n to represent the position of a term in the sequence, where n = 1 for the first term. -10, 40, -160, ... write your answer using decimals and integers. a_n = □(□)^{n - 1} a_4 = □

Explanation:

Step1: Identify the first - term and common ratio

The first - term $a_1=-10$. To find the common ratio $r$, divide the second term by the first term: $r=\frac{40}{-10}=-4$.

Step2: Write the general formula for a geometric sequence

The general formula for a geometric sequence is $a_n=a_1r^{n - 1}$. Substituting $a_1=-10$ and $r = - 4$ into the formula, we get $a_n=-10(-4)^{n - 1}$.

Step3: Find the 4th term

Substitute $n = 4$ into the formula $a_n=-10(-4)^{n - 1}$. Then $a_4=-10(-4)^{4 - 1}=-10\times(-64)=640$.

Answer:

$a_n=-10(-4)^{n - 1}$
$a_4 = 640$