# Thread: arithmatic sequence question and find the term.

1. ## arithmatic sequence question and find the term.

Alright, so first question is: Felicity starts a new job with a salary of 16000 per year. She receives a raise of 850 each year with this company. Calculate her total earnings after fourteen years.

Im stuck with that and have no idea what to do...

And the next is finding the term number.

Determine the value of S19, in other words, 19th term for the following arithmetic series=
(-10)+(-4)+2+...

2. Originally Posted by simplekin
Alright, so first question is: Felicity starts a new job with a salary of 16000 per year. She receives a raise of 850 each year with this company. Calculate her total earnings after fourteen years.

Im stuck with that and have no idea what to do...

And the next is finding the term number.

Determine the value of S19, in other words, 19th term for the following arithmetic series=
(-10)+(-4)+2+...

First year=16000 each month
Second year=16850 each month
Third year=17700 each month

First year=$\displaystyle a$=16000 x 12
Second year=$\displaystyle T_1$=16850 x 12
Third year=$\displaystyle T_2$=17700 x 12

$\displaystyle d=T_2-T_1$

$\displaystyle n=14$

$\displaystyle S_{14}=0.5(14)(2a+13d)$

$\displaystyle (-10)+(-4)+2+...$

$\displaystyle a=-10$
$\displaystyle d=+6$
$\displaystyle n=19$

$\displaystyle S_{19}=0.5(19)(2a+18d)$