# How do you find the sum of the first 10 terms of the arithmetic sequence, if the first term is 5 and the common difference is -8?

Nov 9, 2016

${S}_{10} = - 310$

#### Explanation:

There is a formula for the sum of $n$ terms of an A.P.

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

FRom the information given, we know that:

$n = 10 \text{ " a= 5, " "d = -8" }$ substitute the values

${S}_{10} = \frac{10}{2} \left[2 \left(5\right) - 8 \left(\left(10\right) - 1\right)\right]$

${S}_{10} = 5 \left[10 - 80 + 8\right]$

$S - 10 = 5 \times - 62 = - 310$