Question

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

Answer 1

Answer:

Arithmetic sequence

$a_n=17-3n$

Step-by-step 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

$a_n=17-3n$