#### Question

Given the terms of an arithmetic sequence, a_1=−19 and a_{26}=56 find a formula for the general term.

Question

Let d the common difference of the arithmetic sequence.

Use the formula for general terms,

a_n=a_1+(n-1)d

d=\dfrac{a_n-a_1}{n-1}

=\dfrac{a_{26}-a_1}{26-1}

=\dfrac{56-(-19)}{25}

=\dfrac{75}{25}

=3

Next, use the first term a_1=−19 and the common difference d=3 to find a formula for the general term.

a_n=-19+(n-1)3 =3n-22