I need help on this problem please.

Question

A man gets a job with a salary of $33,000 a year.

He is promised a $2,990 raise each subsequent year.

During a 9-year period his total earnings are $_________.



Answer 1

To find the total earnings you need to find the sum of an arithmetic sequence where the first value is $33,000,

the number of terms is 9 and the difference between values is $2,990.

First we need to find the 9th term of the sequence: a9 = a1 + (n-1)d, where a1 = $33,000, n = 9 and d = $33,000 = $33,000 + 8*$2990 = $56,920.

Then we find the sum of all nine terms: S9 = n(a1 + a9)/2 = 9($33,000 +$56,920)/2 = $404,640.

An alternative formula to find the sum in a single step is: n/2 * (2a + (n-1)*d))