SOLUTION: The sum of the first three terms of a G.P. is 42 and the fourth term exceeds the first by 42. Find the values of the first term and the common ratio.

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Question 1132100: The sum of the first three terms of a G.P. is 42 and the fourth term exceeds the first by 42.
Find the values of the first term and the common ratio.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
(1)  +a+%2B+ar+%2B+ar%5E2+=+42+ 
(2)  +ar%5E3+-+a+=+42+

So we have ++a+%2B+ar+%2B+ar%5E2+=+ar%5E3+-+a+
+1+%2B+r+%2B+r%5E2+=+r%5E3+-+1+
+1+%2B+r+%2B+r%5E2+=+%28r+-+1%29%28r%5E2+%2B+r+%2B+1%29+
++1+=+%28r+-+1%29+

Common ratio:
+highlight%28+r+=+2+%29+

First term:
from (1): +a+%2B+2a+%2B+4a+=+42+ --> a = 6

++highlight%28+a+=+6+%29+


Check:
6 + (2)(6) + (4)(6) = 6 + 12 + 24 = 42 (ok)
8(6) - 6 = 48 - 6 = 42 (ok)