SOLUTION: a G.P has a first term of a, a common ratio of r and its 6th term is 768. another G.P has a first term of a, a common ratio of 6r and its 3rd term is 3456. evaluate a and r.

Question 336304: a G.P has a first term of a, a common ratio of r and its 6th term is 768. another G.P has a first term of a, a common ratio of 6r and its 3rd term is 3456. evaluate a and r.
Answer by galactus(183) (Show Source): You can put this solution on YOUR website!
The nth term of a geometric sequence is given by

For the first condition, the 6th term is 768:

For the second condition, the third term is 3456:

So, we have two equations with two unknowns to solve, a and r:

Solve the first one for and sub into the second one:

Therefore,
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