Dont really understand how to do this

Answers:

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Explanation:

Note we subtract 3 off the previous term (t1) to get the next term (t2). Each new successive term is found this way

and so on. This process may take a while to reach

There's a shortcut. The nth term of any arithmetic sequence is

We plug in and simplify

Then we can plug in various positive whole numbers for n to find the corresponding value. For example, plug in n = 2

which matches with the second term we found earlier. And,

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The notation refers to the sum of the first ten terms

We could use either the long way or the shortcut above to find all through . Then add those values up. Or we can take this shortcut below.

The sum of the first ten terms is -85

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As a check for , here are the first ten terms:

Then adding said terms gets us...

5 + 2 + (-1) + (-4) + (-7) + (-10) + (-13) + (-16) + (-19) + (-22) = -85

This confirms that is correct.