# How do you find the sum of the arithmetic sequence having the data given a_1=7, d = - 3, n = 20?

Mar 5, 2016

The sum  color(blue)(= -430

#### Explanation:

The formula for the sum of an arithmetic sequence when ${a}_{1} , d \mathmr{and} n$ are given is:

color(blue)(Sum = (n/2)[2a + (n-1)d]

Data provided is:
${a}_{1} = 7 , d = - 3 , n = 20$

Here :${a}_{1} = 7 , d = - 3 \mathmr{and} n = 20$

$= \left(\frac{20}{2}\right) \left[2 . 7 + \left(20 - 1\right) . - 3\right]$

$= 10 . \left[14 + 19 . \left(- 3\right)\right]$

$= 10 . \left[14 - 57\right]$

 color(blue)(= -430