The second and fifth term of a geometric progression are 1 and⅛ respectively find the eight term
Let the common ratio of the geometric progression be r. Then:
- The second term is the first term (which we don't know) multiplied by r once, so 1 = ar.
- The fifth term is the first term multiplied by r four times, so 1/8 = ar^4.
We can solve for the first term a by dividing the second equation by the first:
1/8 ÷ 1 = ar^4 ÷ ar
1/8 = r^3
Taking the cube root of both sides, we get:
r = 1/2
Now we can use the formula for the nth term of a GP to find the eighth term:
an = ar^(n-1)
a8 = a1 × r^7
We know a1 = 1 (from the first equation above), so:
a8 = 1 × (1/2)^7
a8 = 1/128
Therefore, the eighth term of the geometric progression is 1/128.