等比數列2條

Since the 5th term is r^3 times the 2nd term, so we have:

8r^3 = 125

r^3 = 125/8

r = 5/2

This yields a geometric progression with common ratio 5/2.

Then the first term is 8/(5/2) = 16/5

To find the 4th term, we use the the the formula ar^(n-1):

(16/5)*(5/2)^(4-1)=50

2. To find the ratio of any two terms, we can divide the 6th term by the 2nd term:

a_6/a_2

=> 4/(1/4) = [r^(6-1)/r^(2-1)]

=> 4/(1/4) = r^(6-2)

=> 16 = r^4

r = 2

Hence the common ratio is 2

b) Then now, solve for the first term:

2nd term = 1st term * common ratio^(2nd term - 1st term)

1/4 = a*(2)^(2-1)

1/4 = a*2

1/8 = a

So, the value of the first term is 1/8.

c) Since the formula for the general term for each geometric progression is a_n = a_1 * r^(n-1)

then substituting a_1 = 1/8, r =2, we have:

a_n = (1/8)*(2)^(n-1)