Solve the problem Suppose you just recieved a job offer with

Solve the problem.

Suppose you just recieved a job offer with a starting salary of #37,000 per year and a guaranteed raise of $1500 per year. How many years will it be before you\'ve made a total (or aggregate) salary of $1,025,000?

Show all work please.

Solution

starting salary = $ 37000

per year raise = $ 1500

this is an arithmetic sequence with common difference = 1500

sum of arithmetic sequence is given by

Sn = n/2 [ 2a + (n-1)d]

plugging the values

1025000 = n/2 [ 2* 37000 + ( n-1) 1500 ]

multiplying both sides by 2

2050000 = n [ 74000 + 1500n - 1500 ]

2050000 = 1500n^2 + 72500n

on solving n we get

n = 20 years

in 20 years salary would be $ 1025000