Question

What is the 8th term of the sequence 48,24,12,6,…….

Answer 1

The given sequence is

48, 24, 12, 6, ...

Let a be the first term of the given sequence.

a=48.

we need to find the common ratio.

consider the first two terms.

`(24)/(48)=(1)/(2)`

Consider the terms 24 and 12.

`(12)/(24)=(1)/(2)`

The common ratio is 1/2.

The given sequence is in the form of geometric progress.

Recall that the formula for the n th term of G.P is

`n\text{ th term=}ar^(n-1)`

Substitute a=48, r=1/2, and n=8 to find the 8 th term.

`8\text{ th term =48(}(1)/(2))^(8-1)`

`8\text{ th term =48(}(1)/(2))^7`

`8\text{ th term =}(48)/(2^7)`

`8\text{ th term =}(48)/(128)^{}=(3)/(8)=0.375`

Hence the 8 th term of the given sequence is 3/8 or 0.4.