Question

Find the common ratio for the geometric sequence for which a1=3 and a5=48

Answer 1

The common ratio for the geometric sequence is:

2

Explanation:

In general, the terms of geometric sequence is given as:

`a,ar,ar^2,ar^3,...`

where a is the first term and r is the common ratio

Here, a=3

and fifth term of geometric sequence=48

i.e.
`ar^4=48`

`3r^4=48\\\\r^4=16\\\\r^4=2^4\\\\r=2`

Hence, the common ratio for the geometric sequence is:

2

Answer 2

The ratio is common, so you could write:

a1 * r^4 = a^5 (you do r^4 because there are 4 times you need to multiply by the ratio to get from a1 to a5)

Plug in the values:

3 * r^4 = 48

Divide by 3:

r^4 = 16

Take the fourth root of both sides:

r = 2

The common ratio is 2.