SOLUTION: An exponential sequence is such that the third term minus the first term is 48. The fourth term minus the second term is 144. Find the common ratio, the first term, the sixth term

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Question 1162270: An exponential sequence is such that the third term minus the first term is 48. The fourth term minus the second term is 144. Find the common ratio, the first term, the sixth term
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let the first term be a, and let r be the common ratio. Then...

The third term minus the first is 48:

ar%5E2-a+=+a%28r%5E2-1%29+=+48 [1]

The fourth term minus the second is 144:

ar%5E3-ar+=+ar%28r%5E2-1%29+=+144 [2]

Dividing [2] by [1] gives us r=3.

Substituting r=3 in [1] gives us a=6.

ANSWERS:

The first term is 6; the common ratio is 3. The 6th term is 6(3^5) = 6*243 = 1458.