The 8th term of a(GP) is 640. If the first term is 5, find the common ratio and the 10th term?
I need the calculation and the answer in the given question
Just a slight workings but give headache
The 8th term of G.P is 640,if the first term is 5, find the common ratio and the 10th term
To find the common ratio and the 10th term of a geometric progression (GP), we can use the formula for the nth term of a GP:
a_n = a * r^(n-1)
where:
a_n = nth term of the GP
a = first term of the GP
r = common ratio
n = term number
Given that the 8th term, a_8, is 640 and the first term, a, is 5, we can substitute these values into the formula:
640 = 5 * r^(8-1)
640 = 5 * r^7
To find the common ratio, we need to isolate r. Let's divide both sides of the equation by 5:
640/5 = r^7
128 = r^7
Now, to find the 10th term, a_10, we can use the same formula, substituting the known values:
a_10 = 5 * r^(10-1)
a_10 = 5 * r^9
Since we know that r^7 = 128, we can substitute this value into the equation for a_10:
a_10 = 5 * (128)^9
To evaluate this expression, raise 128 to the power of 9 and then multiply by 5. The answer to the equation will give you the 10th term of the GP.
I need the calculation and explaination to this question
The 8 term of a g.p is 640 if the common ratio and the tenth term
I have not understand all
5 * r^7 = 640 ... r^7 = 128 ... r = 2
10th term = 5 * 2^9