Question

Determine if it is an arithmetic or geometric sequence:72, 48, 24…Also find the 12th term of the sequence

Answer 1

Given

Determine if it is an arithmetic or geometric sequence:

72, 48, 24…

Solution

Arithmetic Sequence is described as a list of numbers, in which each new term differs from a preceding term by a constant quantity.

Geometric Sequence is a set of numbers wherein each element after the first is obtained by multiplying the preceding number by a constant factor.

`72,48,24`

-24 is the constant quantity, therefore it is an arithmetic sequence

Find the 12th term

formula

`a_n=a_1+(n-1)d`
`\begin{gathered} n=12 \\ a_1=72 \\ d=-24 \end{gathered}`

We can plug in to the formula

`\begin{gathered} a_(12)=72+(12-1)-24 \\ a_(12)=72+(11)-24 \\ a_(12)=72+(-264) \\ a_(12)=72-264 \\ a_(12)=-192 \end{gathered}`

The 12th term of the sequence is -192