SOLUTION: The first three terms of a geometric series are p-1, 2p, and 4p +6 respectively where p is a constant (a) find the value of the constant p (b) calculate the corresponding value o

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Question 662303: The first three terms of a geometric series are p-1, 2p, and 4p +6 respectively where p is a constant
(a) find the value of the constant p
(b) calculate the corresponding value of the common ratio
(c) Find the sum to ten terms of the series
Answer by KMST(5328) About Me  (Show Source):
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The common ratio, is the ratio between consecutive terms in a geometric sequence, and it is constant, so
2p%2F%28p-1%29=%284p%2B6%29%2F2p --> 4p%5E2=%28p-1%29%284p%2B6%29 equating the cross-products
4p%5E2=%28p-1%29%284p%2B6%29 --> 4p%5E2=4p%5E2%2B2p-6 --> 0=2p-6 --> 2p=6 --> highlight%28p=3%29

The first three terms are
p-1=3-1=2
2p=2%2A3=6 and
4p%2B6=4%2A3%2B6=12%2B6=18
The common ratio is 6%2F2=highlight%283%29

The sum of the first n terms of a geometric sequence with first term A
and common ratio r is
a%2A%28%28r%5En-1%29%2F%28r-1%29%29
In this case, it is 2%2A%28%283%5E10-1%29%2F%283-1%29%29=2%2A%2859049-1%29%2F2=highlight%2859048%29