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karen's new year's resolution is to work out each day on her elliptical. the number of calories she has burned each day since she started is shown below. write a rule for the sequence, and find the number of calories that karen will burn on the 30th day.

Given that the number of calories that Karen burned each day since she started is given by sequence {349, 357, 365, 373, 381,...}

Now we have to find a rule for the given sequence.

Most of the sequences are usually AP or GP so let's test for AP.

In AP, difference between consecutive terms is always equal.

357-349=8

365-357=8

373-365=8

381-373=8

We can see that each time difference is fixed to 8.

Hence given sequence is an AP whose common difference d=8

First term a=349

Now the rule can be written using nth term formula which is

plug the given values

Hence required rule is where n is natural number.

Now we ahve to find the number of calories that Karen will burn on the 30th day. So plug n=30 in above rule

Hence final answer is 581 calories.

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