# Find the function if the second term in an arithmetic sequence is 5 and the fifth term is 68

Find the function if the second term in an arithmetic sequence is 5 and the fifth term is 68
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scranna0o
The general term of an arithmetic sequence is given by the formula:
${a}_{n}=a+d\left(n-1\right)$
where a is the initial term and d the common difference.
We find:
$3d=\left(a+4d\right)-\left(a+d\right)={a}_{5}-{a}_{2}=68-5=63$
Dividing both ends by 3 we get:
$d=21$
Then:
${a}_{1}=a=\left(a+d\right)-d={a}_{2}-d=5-21=-16$
So the formula for the general term can be written:
${a}_{n}=-16+21\left(n-1\right)=21n-37$