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Video: Solving Word Problems Involving Arithmetic Sequences

Bethani Gasparine

Jane charges $7.25 for an hour of babysitting. The sequence 7.25, 14.5, 21.75, 29, ... represents how much she charges for 𝑛 hours. Determine the next three terms in the sequence, and find how much she charges for 14 hours of babysitting.

02:53

Video Transcript

Jane charges seven dollars and 25 cents for an hour of babysitting. The sequence 7.25, 14.5, 21.75, 29 represents how much she charges for 𝑛 hours. Determine the next three terms in the sequence and find how much she charges for 14 hours of babysitting.

Here, we have our sequence 7.25, 14.5, 21.75, 29, and then the next three terms in the sequence that we will be finding. In order to find how much she charges for 14 hours of babysitting, we can use 7.25 times 𝑛, where 𝑛 is in hours. Let’s first begin with the sequence. 7.25 is equal to 7.25 times one. 14.5 is equal to 7.25 times two. 21.75 is equal to 7.25 times three. And 29 is equal to 7.25 times four.

So our sequence uses 7.25 times 𝑛, the number of hours that she babysat. So we’ve already used 𝑛 equal to one, two, three, and four. So the next number in the sequence will be 36.25 because that is 7.25 times five. The next number will be 43.5 because it is 7.25 times six. And lastly, we have 50.75 because that is equal to 7.25 times seven.

So the next three terms in the sequence were 36.25, 43.5, and 50.75. Lastly, we are supposed to find how much she charges for 14 hours of babysitting. So we need to take 7.25 times 14 because 14 is the number of hours, and that’s what we plug in for 𝑛. Therefore, she charges 101 dollar and 50 cents for 14 hours of babysitting.

So our final sequence is 7.25, 14.5, 21.75, 29, 36.25, 43.5, 50.75. And finally, she would charge 101 dollars and 50 cents for 14 hours of babysitting.