Question

given the explicit formula for an arithmetic sequence find the first five terms and the term named in the problem. (a_{1}=-34), (d = - 10). (a_{2}=) type your answer. (a_{3}=) type your answer. (a_{4}=) type your answer. (a_{5}=) type your answer. (a_{6}=) 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 $n = 2$, $a_{1}=-34$, and $d=-10$ into the formula:
$a_{2}=a_{1}+(2 - 1)d=-34+(1)\times(-10)=-34 - 10=-44$

Step3: Find $a_{3}$

Substitute $n = 3$, $a_{1}=-34$, and $d=-10$ into the formula:
$a_{3}=a_{1}+(3 - 1)d=-34+(2)\times(-10)=-34-20=-54$

Step4: Find $a_{4}$

Substitute $n = 4$, $a_{1}=-34$, and $d=-10$ into the formula:
$a_{4}=a_{1}+(4 - 1)d=-34+(3)\times(-10)=-34 - 30=-64$

Step5: Find $a_{5}$

Substitute $n = 5$, $a_{1}=-34$, and $d=-10$ into the formula:
$a_{5}=a_{1}+(5 - 1)d=-34+(4)\times(-10)=-34-40=-74$

Step6: Find $a_{6}$

Substitute $n = 6$, $a_{1}=-34$, and $d=-10$ into the formula:
$a_{6}=a_{1}+(6 - 1)d=-34+(5)\times(-10)=-34-50=-84$

Answer:

$a_{2}=-44$
$a_{3}=-54$
$a_{4}=-64$
$a_{5}=-74$
$a_{6}=-84$