The 8th term of a GP is 640 if the 1st term is 5 find the common ratio and the 10th term
To find the common ratio (r), we can use the formula for the nth term of a GP:
an = a1 * r^(n-1)
where an is the nth term, a1 is the 1st term, r is the common ratio, and n is the number of terms.
Using the given information, we know that:
a8 = 640
a1 = 5
n = 8
Substituting the values into the formula, we get:
640 = 5 * r^(8-1)
640 = 5 * r^7
r^7 = 128
r = 2
So the common ratio is 2.
To find the 10th term, we can again use the formula for the nth term:
a10 = a1 * r^(10-1)
Substituting the values, we get:
a10 = 5 * 2^(10-1)
a10 = 5 * 2^9
a10 = 5 * 512
a10 = 2560
So the 10th term is 2560.