Question

given the explicit formula for an arithmetic sequence find the first five terms and the term named in the problem. (a_{1}=35), (d = 4). (a_{2}=) type your answer.. (a_{3}=) type your answer.. (a_{4}=) type your answer.. (a_{5}=) type your answer.. (a_{n}=) type your answer..

Explanation:

Step1: Recall arithmetic - sequence formula

The formula for the $n$th term of an arithmetic sequence is $a_n=a_1+(n - 1)d$. We know $a_7=a_1+(7 - 1)d=35$ and $d = 4$.

Step2: Find $a_1$

Substitute $d = 4$ into $a_7=a_1+6d=35$. So $a_1+6\times4=35$, then $a_1=35 - 24=11$.

Step3: Find $a_2$

Use the formula $a_n=a_1+(n - 1)d$. For $n = 2$, $a_2=a_1+(2 - 1)d=11 + 4=15$.

Step4: Find $a_3$

For $n = 3$, $a_3=a_1+(3 - 1)d=11+2\times4=11 + 8=19$.

Step5: Find $a_4$

For $n = 4$, $a_4=a_1+(4 - 1)d=11+3\times4=11 + 12=23$.

Step6: Find $a_5$

For $n = 5$, $a_5=a_1+(5 - 1)d=11+4\times4=11 + 16=27$.

Step7: General formula for $a_n$

Since $a_1 = 11$ and $d = 4$, $a_n=11+(n - 1)\times4=11+4n-4=4n + 7$.

Answer:

$a_2 = 15$
$a_3 = 19$
$a_4 = 23$
$a_5 = 27$
$a_n=4n + 7$