Question

Identify each sequence as arithmetic or geometric. Explain your answer, and write an explicit formula for the

sequence.
a. 14, 11, 8, 5, …

Answer 1

Arithmetic sequence

`a_n=17-3n`

Explanation:

We are given that a sequence

14,11,8,5,...

We have to identify sequence as arithmetic or geometric and write explicit formula for the sequence.

`a_1=14`

`a_2=11`

`a_3=8`

`d_1=a_2-a_1=11-14=-3`

`d_2=a_3-a_2=8-11=-3`

`d_3=a_4-a_3=5-8=-3`

`d_1=d_2=d_3=-3`

When the difference of consecutive terms is constant then the sequence is arithmetic sequence.

Hence, the sequence is an arithmetic sequence.

`a_n=a+(n-1)d`

substitute the values then we get

`a_n=14+(n-1)(-3)=14-3n+3=17-3n`

Then, the explicit formula is given by

`a_n=17-3n`