Question

find the 15th term of the arithmetic sequence whose common difference is d = - 6 and whose first term is a1 = 3.

Explanation:

Step1: Recall the formula for the nth term of an arithmetic sequence

The formula for the $n$th term of an arithmetic sequence is $a_n=a_1+(n - 1)d$, where $a_n$ is the $n$th term, $a_1$ is the first - term, $n$ is the term number, and $d$ is the common difference.

Step2: Identify the given values

We are given that $a_1 = 3$, $n = 15$, and $d=-6$.

Step3: Substitute the values into the formula

Substitute $a_1 = 3$, $n = 15$, and $d=-6$ into the formula $a_n=a_1+(n - 1)d$.
$a_{15}=3+(15 - 1)\times(-6)$

Step4: Simplify the expression inside the parentheses first

$15−1 = 14$, so the expression becomes $a_{15}=3+14\times(-6)$.

Step5: Multiply 14 and -6

$14\times(-6)=-84$, so $a_{15}=3-84$.

Step6: Subtract to find the 15th term

$3-84=-81$.

Answer:

$-81$