# How do you find the first term of the arithmetic sequence having the data given a_n= 48, S_n= 546, n = 26?

First term$\text{ " } {a}_{1} = - 6$

#### Explanation:

The given data: ${a}_{n} = 48$ and ${S}_{n} = 546$ and $n = 26$

Formulas for the Sum of n terms of an Arithmetic Sequence

$S n = \frac{n}{2} \left({a}_{1} + {a}_{n}\right)$

$546 = \frac{26}{2} \left({a}_{1} + 48\right)$

solving for ${a}_{1}$

${a}_{1} = - 6$

God bless you ...