# The first term in an arithmetic sequence is 9. The fourth term in the sequence is 24.the twentieth ter is 104. What is the common difference of this sequence? How do you find the nth term of the arithmetic sequence?

The first term in an arithmetic sequence is 9. The fourth term in the sequence is 24.the twentieth ter is 104. What is the common difference of this sequence? How do you find the nth term of the arithmetic sequence?
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pierretteA
Step 1 Given, The first term in an arithmetic sequence is 9. The fourth term in the sequence is 24. And the twentieth term is 104.We know that, The general term of the arithmetic sequence is given by ${a}_{n}=a+\left(n-1\right)$ where d is the common difference a is the first term n is the number of terms Step 2 Now, First term in an arithmetic sequence is 9. $a=9$ The fourth term in the sequence is 24 and the twentieth term is 104 $a+3d=24anda+19d=104$ Put $a=9$ then $⇒9+3d=24$
$⇒3d=24-9$
$⇒3d=15$
$⇒d=5$ The general term of the arithmetic sequence is ${a}_{n}=a+\left(n-1\right)d$
$⇒{a}_{n}=9+\left(n-1\right)5$
$⇒{a}_{n}=9+5n-5$
$⇒{a}_{n}=5n+4$
$\therefore$ The nth term of the arithmetic sequence is ${a}_{n}=5n+4$