Final answer:
The common ratio for the G.P is 2, and the 10th term of the sequence is 2560. The formula for the nth term of a G.P was used to find both values.
Step-by-step explanation:
The given sequence is a geometric progression (G.P), and the 8th term is given as 640, while the first term (a) is 5. The common ratio (r) can be found using the formula for the nth term of a G.P, which is an = a * r(n-1).
Applying this formula to find r:
640 = 5 * r(8-1)
640 = 5 * r7
r7 = 640 / 5
r7 = 128
Now we find the 7th root of 128 to get r:
r = 2
To find the 10th term (a10), we use the formula again with n=10:
a10 = 5 * 2(10-1)
a10 = 5 * 29
a10 = 5 * 512
a10 = 2560