The second and fifth terms of a geometric progression are 1 and 1/8 respectively:find the;
(a) common ratio
(b) first term
(c)eighth term
(a) To find the common ratio (r) we can use the formula for the nth term of a geometric progression:
an = a1 * r^(n-1)
Given that the second term is 1 and the fifth term is 1/8, we have:
a2 = a1 * r = 1
and
a5 = a1 * r^4 = 1/8
Dividing these two equations, we get:
(r^4) / r = 1 / 8
r^3 = 1/8
r = (1/8)^(1/3)
r = 1/2
So the common ratio (r) is 1/2.
(b) To find the first term (a1), we can use the second term formula:
a2 = a1 * r
1 = a1 * 1/2
a1 = 2
So the first term is 2.
(c) To find the eighth term, we can use the nth term formula again:
a8 = a1 * r^(8-1)
a8 = 2 * (1/2)^7
a8 = 2 * (1/128)
a8 = 1/64
So, the eighth term is 1/64.