Question

Your friend asks you to make picture frames and will give you 5 nickels for the first frame. You agree to help if she multiplies your payment by 5 for each frame completed. After 2 frames, you will receive 25 nickels, and after 3 frames, you will receive 125 nickels.

Complete and solve the equation that finds the number of nickels she will pay you after making the tenth frame.when you make the equation can you show me the exponent you use to get this?

Answer 1

I will receive 9,765,625 nickels

Explanation:

multiply 25 x 5= 125 then multiply 125 x 5 all the way till u get to the 10th frame

Answer 2

The cost of making the 10th frame is 9765625

Explanation:

Topic: Geometric Progression

Literally, what is being asked in the question is to get the 10th term of a geometric progression.

This can be done in two ways.

The first way is by multiplying 5 in 10 places;

i.e.
`5^(10) = 9765625`

But what if we're dealing with a kind of difficult combination of numbers.

Follow the highlighted steps below, to solve this question.

Given:

Cost of first frame = 5 nickels

Additional frame cost a multiple of 5

We're to calculate the payment for making 10 frames;

Using the geometric Formula

`T_(n) = ar^(n-1)`

Where a = first term = cost of first nickel = 5

r = common ratio = multiple of 5

n = 10th nickel

Tn = Cost of the tenth nickel; i.e
`T_(10)`

By Substitution

`T_(n) = ar^(n-1)` becomes

`T_(10) = 5 * 5^(10-1)`

`T_(10) = 5 * 5^(9)`

`T_(10) = 5 * 1953125`

`T_(10) = 9765625`

Hence, the cost of making the 10th frame is 9765625