8. The sum of four integers in A.P. is 24 and their product is 945. Find them.
[Hint. Select the numbers to be a - 3d, a-d, a + d, and a + 3d
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Answer:
the sum of four integers
a-3d +a-d+a+d +a+3d=24
a+a+a+a-3d-d+d+3d =24
4a-4d+4d=24
4a=24
a=24/4
a=6
And the product
a-3d (a-d)+a+d (a+3d)=945
a (a-d)-3d (a-d)+a (a+3d)+d (a+d)=945
a^2-ad-3ad+3d^2 +a^2+3ad+da+d^2=945
a^2+a^2-ad-3ad+3ad+ad+3d^2+d^2=945
2a^2+4d^2=945
2a+4d=945
2a+d=945/4
2a+d =236
a+d=236/2
ad=118
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