# Arithmetic Sequence

**Topics:**Geometric progression, Sequence, Mathematics

**Pages:**3 (418 words)

**Published:**October 12, 2011

Allana Robinson

MAT 126

Survey of Mathematical Methods

Melinda Hollingshed

August 21, 2011

Arithmetic Sequence is a sequence of numbers in which each succeeding term differs from the preceding term by the same amount. This amount is known as the common difference and can be found using a specific formula by substituting the numbers from the word problem into the equation. When you plug in all the information, you are able to find out the money that needs to be spent and saved in the following word problems.

35. A person hired a firm to build a CB radio tower. The firm charges $100 for labor for the first 10 feet. After that, the cost of the labor for each succeeding 10 feet is $125 more than the preceding 10 feet will cost $125, the next ten feet will cost $150 etc. How much will it cost to build a 90 foot tower?

an=a1+ (n-1) d

a125=100+ (125-1) (150)

a125=100+124(150)

a125=100+18600

a125=18700

sn =n (a1 + an) / 2

= 125 (100+18700) /2

=125(1880) /2

=62.5 (18800) =1175000

The cost to build a 90-foot tower is $11,750.

37. A person deposited $500 in a savings account that pays 5% annual interest that is compound yearly. At the end of 10 years, how much money will be in the savings account?

S+ (0.5) S n=10

S+ (1+0.5) r=1.05

S (1.05) a1= 500(1.05) =525

an= a1(rn-1)

a10=525(1.05-9)

a10=525(1.551328216)

a10=814.4473134

The balance in the savings account at the end of 10 years will be $814.44.

I chose to use the Arithmetic and geometric sequence because the formula made the answer easier to find the first term and the common difference. All you needed to do was find the formula and plug the numbers from the word problem to get the answer. I could apply this knowledge to real world situations because you can use this when you are checking to see how much money will be in your savings account and how much money...

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