SOLUTION: Geometric Series Question:
a, a-12, a+12 are the first three terms of a geometric sequence
1) What is the value of a?
2) Calculate the sum for the first 10 terms
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-> SOLUTION: Geometric Series Question:
a, a-12, a+12 are the first three terms of a geometric sequence
1) What is the value of a?
2) Calculate the sum for the first 10 terms
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Question 1096580: Geometric Series Question:
a, a-12, a+12 are the first three terms of a geometric sequence
1) What is the value of a?
2) Calculate the sum for the first 10 terms Answer by ikleyn(52790) (Show Source):
Since a, a-12 and a+12 are three consecutive terms of an geometric progression, you have
= . ( the ratio is the same as the ratio )
Then cross-nultiplying
= a*(a+12) ====>
a^2 - 24a + 144 = a^2 + 12a ====>
-24a + 144 = 12a ====> 144 = 24a + 12a ====> 144 = 36a ====> a = = 4.
Your GP is 4, 4-12 = -8, 4+12 = 16.
It has the first term 4 and the common difference (-2).
