Final answer:
To find the common ratio, use the formula for the nth term of a geometric progression. The common ratio is 2, and the 10th term is 2560.
Step-by-step explanation:
To find the common ratio, we can use the formula for the nth term of a geometric progression (GP):
an = a1 * r^(n-1)
Given that the first term (a1) is 5 and that the 8th term (a8) is 640, we can plug these values into the formula and solve for the common ratio (r):
640 = 5 * r^(8-1)
Dividing both sides by 5, we get:
128 = r^7
Taking the 7th root of both sides, we find that the common ratio is 2 (since 2^7 = 128).
To find the 10th term, we can plug the value of the common ratio (r = 2) into the formula again:
a10 = 5 * 2^(10-1)
Simplifying, we get:
a10 = 5 * 2^9 = 5 * 512 = 2560