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.

Algebra ->  Sequences-and-series -> 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.      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
The nth term of a geometric sequence is given by
an=a1%2Ar%5E%28n-1%29
For the first condition, the 6th term is 768:
a6=a1%2Ar%5E5=768
For the second condition, the third term is 3456:
a3=a1%2A36r%5E2=3456
So, we have two equations with two unknowns to solve, a and r:
a1%2Ar%5E5=768
a1%2Ar%5E2=96
Solve the first one for a1=768%2Fr%5E5 and sub into the second one:
%28768%2Fr%5E5%29%2Ar%5E2=96
768%2Fr%5E3=96
r=2
Therefore, a1=24