Question

find the 62nd term of the arithmetic sequence -27, -21, -15, ...

Explanation:

Step1: Identify first - term and common - difference

The first term $a_1=-27$, and the common difference $d=-21 - (-27)=6$.

Step2: Use the formula for the nth term of an arithmetic sequence

The formula for the $n$th term of an arithmetic sequence is $a_n=a_1+(n - 1)d$. Substitute $n = 62$, $a_1=-27$, and $d = 6$ into the formula: $a_{62}=-27+(62 - 1)\times6$.

Step3: Simplify the expression

First, calculate $62-1 = 61$. Then, $61\times6=366$. So, $a_{62}=-27 + 366$.

Step4: Get the final result

$-27+366 = 339$.

Answer:

$339$