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

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) (Show Source): You can put this solution on YOUR website!
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 . The 15 comes from

So our first equation is

The second term is and the fifth term is , so the second equation is:

, which simplifies to

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

Substitute this value for d into the first equation:

Check:

Answer checks.
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