the 8th term of a Gp 640 if the first term is 5 find the common ratio and the 11th term
today
ar^7 / a = r^7 = 640/5 = 128 = 2^7
r = 2
Now find ar^10 = 640 * 2^3
To find the common ratio (r) of a geometric progression (GP), we can use the formula:
An = A1 * r^(n-1)
where An is the nth term, A1 is the first term, and r is the common ratio.
Given that the first term (A1) is 5 and the 8th term (A8) is 640, we can substitute these values into the formula:
A8 = A1 * r^(8-1)
640 = 5 * r^7
To find r, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 5:
640/5 = r^7
128 = r^7
To solve for r, we can take the 7th root of both sides:
r = (128)^(1/7)
Using a calculator, we find that r is approximately 2.
Now, to find the 11th term (A11), we can use the formula again:
A11 = A1 * r^(11-1)
A11 = 5 * 2^10
A11 = 5 * 1024
A11 is approximately 5120.