# How do you find the sum of the arithmetic sequence having the data given a_1=5, d = -2, n = 12?

Feb 22, 2016

The sum:
${S}_{12} = - 72$

#### Explanation:

The first term: ${a}_{1} = 5$

The common difference: $d = - 2$

Number of terms of the sequence: $n = 12$

The sum of $n$ terms of arithmetic sequence is found using formula:

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

${S}_{n} = \frac{12}{2} \left[2 \times 5 + \left(12 - 1\right) \times - 2\right]$

$= 6 \left[10 + \left(11\right) \times - 2\right]$

$= 6 \left[10 - 22\right]$

$= 6 \times - 12$

${S}_{12} = - 72$