Question

given the explicit formula for an arithmetic sequence find the first five terms and the term named in the problem.
a1 = - 38
d = - 100
a2 = type your answer...
a3 = type your answer...
a4 = type your answer...
a5 = type your answer...
an = type your answer...

Explanation:

Step1: Recall arithmetic - sequence formula

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

Step2: Find $a_{2}$

Substitute $n = 2$, $a_{1}=-38$, and $d=-100$ into the formula:
$a_{2}=a_{1}+(2 - 1)d=-38+(1)\times(-100)=-38 - 100=-138$.

Step3: Find $a_{3}$

Substitute $n = 3$, $a_{1}=-38$, and $d=-100$ into the formula:
$a_{3}=a_{1}+(3 - 1)d=-38+(2)\times(-100)=-38-200=-238$.

Step4: Find $a_{4}$

Substitute $n = 4$, $a_{1}=-38$, and $d=-100$ into the formula:
$a_{4}=a_{1}+(4 - 1)d=-38+(3)\times(-100)=-38 - 300=-338$.

Step5: Find $a_{5}$

Substitute $n = 5$, $a_{1}=-38$, and $d=-100$ into the formula:
$a_{5}=a_{1}+(5 - 1)d=-38+(4)\times(-100)=-38-400=-438$.

Step6: Find the general formula for $a_{n}$

Substitute $a_{1}=-38$ and $d=-100$ into the formula $a_{n}=a_{1}+(n - 1)d$:
$a_{n}=-38+(n - 1)\times(-100)=-38-100n + 100=62-100n$.

Answer:

$a_{2}=-138$
$a_{3}=-238$
$a_{4}=-338$
$a_{5}=-438$
$a_{n}=62 - 100n$