Final answer:
To find the 4th term of a GP with the 1st term of 5 and the 3rd term of 80, we first determined the common ratio to be 4. Then, using the common ratio, we calculated the 4th term to be 320.
Step-by-step explanation:
To find the 4th term of a geometric progression (GP) when the 1st and 3rd terms are given as 5 and 80, respectively, we first need to find the common ratio of the progression.
We know that in a GP, the nth term is given by an = a1 × r(n-1), where a1 is the first term and r is the common ratio.
Given that the 3rd term a3 is 80, we can use the formula to write a3 = a1 × r(3-1) = 5r2, and thus:
r = √(80/5) = √(16) = 4.
Now, to find the 4th term (a4), we use the common ratio r = 4 and the first term a1 = 5:
a4 = a1 × r(4-1) = 5 × 43 = 5 × 64 = 320.
Therefore, the 4th term of the GP is 320.