The 8th term of a geometric progression is -7/32. Find it's common ratio if it's first term is 28?
r^7 = (-7/32)/28 = -1/128
r = -1/2
and that's its, not it's
Just like his and hers, not hi's and her's
Fine the common ratio and the 8th term
To find the common ratio of a geometric progression, we need to use the formula for the nth term of a geometric sequence.
The formula for the nth term of a geometric sequence is:
an = a1 * r^(n-1)
In this case, we're given the 8th term, so n = 8. We know that the first term (a1) is 28, and the 8th term (a8) is -7/32.
So, we can substitute these values into the formula:
-7/32 = 28 * r^(8-1)
Simplifying the equation, we have:
-7/32 = 28 * r^7
Now, we can isolate the common ratio (r) by solving for it:
r^7 = (-7/32) / 28
To solve for r, we take the 7th root of both sides:
r = ( (-7/32) / 28 )^(1/7)
Simplifying further, we have:
r = -1/2
So, the common ratio of the geometric progression is -1/2.