SOLUTION: The sum of five numbers in an Arithmetic Progression is 25 and the sum of their squares is 165. Find the common difference.

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Question 1047950: The sum of five numbers in an Arithmetic Progression is 25 and the sum of their squares is 165. Find the common difference.
Found 2 solutions by robertb, ikleyn:
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
S%5B5%5D+=+25+=+2a%5B1%5D%2B4d ===> a%5B1%5D+=+5-2d

===> a%5B1%5D%5E2+%2B+a%5B2%5D%5E2+%2B+a%5B3%5D%5E2++%2B+a%5B4%5D%5E2+%2B+a%5B5%5D%5E2++=+165
<===> %285-2d%29%5E2+%2B+%285-d%29%5E2+%2B5%5E2+%2B+%285%2Bd%29%5E2+%2B+%285%2B2d%29%5E2+=+165
After expanding each term accordingly, you should get
125+%2B+10d%5E2+=+165
===> d%5E2+=+4
===> d = 2 or -2.
(If d = 2, the sequence is 1,3,5,7,9. If d = -2, the sequence is 9,7,5,3,1. These are two different sequences, both of which
satisfy the initial conditions.)

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Similar problem was solved in
https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.979908.html

https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.979908.html