Question

How do you find `S_n` for the arithmetic series given `a_1=3`, d=-4, n=8?

Answer 1

`S_8 = -100`

Explanation:

As a last resort you could write out the sequence (because you have `a_1 and d`) and then add the first 8 terms together.

However this is not practical, especially if there are many terms....
and while it is a method which produces a correct answer, it lacks style and shows little understanding of working with sequences.

There is a formula which shows exactly what you need to know and what you need to do:

`S_n = n/2(a_1 +d( n-1)`

`a_1 = 3" "d = -4" "n = 8`

`S_8 = 8/2(3 -4(8-1))`

`S_8= 4(3-4(7))`

`S_8 =4(3-28)`

`S_8 = 4 xx -25`

`S_8 = -100`