Question

What is the sum of the first 14 terms of the sequence -11+(-18)+(-25)+(-32)...

Answer 1

The difference between -11 and -18 is -7
the difference between -18 and -25 is -7
the difference between -25 and -32 is -7

therefore we can say that the difference between all of the terms will be -7.

the first term is -11 -> call this a
the difference is -7 -> call this d
the number of terms is 14 -> call this n

use the equation (sum of)$_{n}$ = $\frac{n}{2}$(2a + (n-1)d)

(sum of)$_{n}$ = $\frac{14}{2}$(2 x -11 + (14-1)-7)

= -7(-22 + (13 x -7))
= -7(-22 + -91)
= -7(-111)
= 777