Question

What is the explicit formula for the sequence: 32, 48, 72, 108,..

Answer 1

• 48/32=3/2
• r=3/2
• a=32

Verify with next one

• 48(3/2)=72

Verified

formula

`\\ \tt\hookrightarrow a_n=ar^(n-1)`

`\\ \tt\hookrightarrow a_n=32(3/2)^(n-1)`

Answer 2

`a_n=32 \cdot \left(\frac32 \right)^(n-1)`

Explanation:

The difference between each term in the sequence is not the same, therefore the sequence is a geometric sequence.

Geometric sequence formula:
`a_n=a r^(n-1)`

where
`a` is the start term and
`r` is the common ratio

Given
`a = 32`

To calculate
`r`, divide one term by its previous term:

`\implies r=(a_4)/(a_3)=(108)/(72)=\frac32`

Therefore,
`a_n=32 \cdot \left(\frac32 \right)^(n-1)`