# How do you find the first term of the arithmetic sequence given an = 48, Sn = 546, n = 26?

Aug 31, 2015

 a_1=color(blue)(-6

#### Explanation:

We are provided with:
${a}_{N} = 48$
${S}_{n} = 546$
$n = 26$

The formula for sum of an Arithmetic Sequence when the sum ${s}_{n}$, number of terms $n$ and last term ${a}_{n}$ are given is:

 color(blue)(S_n = (n/2)(a_1+a_n)

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

$546 \cdot \frac{2}{26} = a + 48$

$21 \cdot 2 = a + 48$

${a}_{1} = 42 - 48$

 a_1=color(blue)(-6