SOLUTION: The sum of the first six terms of an A.P is 72 and the second term is seven times the fifth term. Form two equations in a' and d' and solve them to find the first term and the comm

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Question 127233: The sum of the first six terms of an A.P is 72 and the second term is seven times the fifth term. Form two equations in a' and d' and solve them to find the first term and the common diffrence. Thanks and pls help!
Answer by solver91311(24713) About Me  (Show Source):
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The first term is a, the second term is a + d, the third, a + 2d, etc.

So the sum of the first 6 terms is 6a%2B15d. The 15 comes from 1%2B2%2B3%2B4%2B5=15

So our first equation is 6a%2B15d=72

The second term is a%2Bd and the fifth term is a%2B4d, so the second equation is:

a%2Bd=7%28a%2B4d%29, which simplifies to -6a-27d=0

Add the two equations, since the coefficients on the a terms are already additive inverses

0a-12d=72
d=-6

Substitute this value for d into the first equation:

6a%2B15%28-6%29=72
6a=72%2B90
a=27

Check:

27%2B21%2B15%2B9%2B3-3=72

21=7%283%29

Answer checks.