Ira S. answered • 04/04/17

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The formula for an arithmetic sequence is a

_{n}= a_{1}+ d(n-1). You know it's arithmetic since this is repeated addition.You know a

_{1}= -9 and d= 5, so your sequence has the formula a_{n}= -9+5(n-1) = 5n-14So now you can set that equal to 66 to find out which term number this is.

5n-14=66

5n = 80

n=16

So the 16th term is 66.

So you have the summation from 1 to 16 of the expression 5n-14.

Unfortunately, this is not one of your choices....so they have a different form of this answer. All summations can be changed with respect to their indeces.

So if we switch the indeces to vary from 0 to 15, we must change the function by adding 5.

So you get the summation from 0 to 15 of the expression 5n-9.

Hope this helped.