Anonymous
Anonymous asked in Science & MathematicsMathematics · 7 months ago

# Help with Arithmetic Series?

Corey is deciding between two summer jobs. He plans to work from May to August, inclusive.

First job pays \$1500/month with a monthly raise of \$150

Second job pays \$300/week with a weekly raise or \$15

a. Determine the total income earned if Corey takes the first job

b. How many weeks are there during this time period

c. Determine the total income earned if Corey takes the second job

Relevance
• from May to August (July 31) is 3 months, 13 weeks.

Job1 \$4,950. 13 weeks. Job 2 \$5,100.

• To make the arithmetic a little easier we will assume the duration is 3 months or 12 weeks

(Job 1) We have an arithmetic series with first term 1500 and common difference 150

so, S₃ = (3/2)[3000 + 2(150)] = (3/2)[3000 + 300)

i.e. \$4950

(Job 2) We have an arithmetic series with first term 300 and common difference 15

so, S₁₂ = (12/2)[600 + 11(15)] = 6[600 + 165]

i.e. \$4590

Therefore, earning \$360 more doing the first job.

:)>

• May to Aug is 4 months, and 31•3+30 = 123 days, or 17 weeks 4 days

unclear if you want me to use 17 or 18 weeks

also depends on when pay week starts and ends, on which day....

first job pays 1500+1650+1800+1950 = 6900           or 1500•4 + 150•6 = 6900sec job pays (at 17 weeks)

300+315+330...

use sum of series, d=15, a = 300, n = 17

S = (n/2)(2a+d(n–1)) = (17/2)(2•300+15(16)) = 8.5(600+225) = 7140

(18 weeks)

(18/2)(2•300+15(18)) = 9(600+270) = 7830

Arithmetic Series is a sequence of numbers such that the

difference between the consecutive terms is constant.

a + (a+d) + (a+2d) + (a+3d) + ...

Sum of first n terms is

S = (n/2)(a + an)

S = (n/2)(2a+d(n–1))

where an is the nth term

•  Corey is deciding between two summer jobs.

He plans to work from May to August, inclusive.

The first job pays \$1500/month with a monthly rise of \$150.

The second job pays \$300/week with a weekly raise of \$15.

a.

The total income earned if Corey takes the first job is \$6450.

b.

There are 17 weeks during this time period.

c.

The total income earned if Corey takes the second job is \$5355.