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

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

Uniteasy Admin · Accepted Answer

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

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