The common ratio of a G.P. is 2. If the 5th term is
greater than the 1st term by 45, find the 5th term,

Answer Details

Let the first term of the G.P. be a.
The formula for the nth term of a G.P. with first term a and common ratio r is given by:
an = ar^(n-1)
Since the common ratio is 2, the 5th term will be a x 2^(5-1) = 16a.
It is given that the 5th term is greater than the 1st term by 45. Therefore,
16a - a = 45
Simplifying this equation gives:
15a = 45
Dividing both sides by 15 gives:
a = 3
Therefore, the 5th term is 16a = 16 x 3 = 48.
Hence, the answer is 48.