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The sum of the first three terms of an arithmetic sequence is 39, and the sum of the last four terms is 178. If the first term is 10, then what is the average of all the terms?

 Jun 3, 2022
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39==3/2*[20 + 2D], solve for D
178==4/2 * [2F + 3*3 ], solve for F


D ==3 - this is the common difference
F ==40 - this is the first term of the last 4 terms.
Sequence: 10, 13, 16.............40, 43, 46, 49...


Your full sequence looks like this:
10 , 13 , 16 , 19 , 22 , 25 , 28 , 31 , 34 , 37 , 40 , 43 , 46 , 49 , >>Number of terms = 14>>Total Sum == 413


The average of all 14 terms==413 / 14 ==29.5

 Jun 5, 2022

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