Asked by Ore
The fifth term of a geometric progression is 16 and the tenth term is 54 .find the first term and common ratio and find the fifteenth term
Answers
Answered by
oobleck
there are 5 terms between 16 and 54, so r^5 = 54/16 = 27/8
This would have been a lot easier if it had been the 8th term, instead of the 10th, right? Then we'd have had r = 3/2
But now we have r = (3/2)^(3/5)
so a = 16 * r^-4 = 16 * (2/3)^(12/5)
a_15 = a_10 * r^5 = 54 * 27/8 = 729/4
This would have been a lot easier if it had been the 8th term, instead of the 10th, right? Then we'd have had r = 3/2
But now we have r = (3/2)^(3/5)
so a = 16 * r^-4 = 16 * (2/3)^(12/5)
a_15 = a_10 * r^5 = 54 * 27/8 = 729/4
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