Question

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

Answer 1

Answer:

Arithmetic sequence

$a_n=\frac{1}{2}-n$ for $n\geq 1$

Step-by-step explanation:

We are given that a sequence

$-\frac{1}{2},-\frac{3}{2},-\frac{5}{2},-\frac{7}{2},...$

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

$a_1=-\frac{1}{2}$

$a_2=-\frac{3}{2}$

$a_3=-\frac{5}{2}$

$a_4=-\frac{7}{2}$

$d_1=a_2-a_1=\frac{-3}{2}+\frac{1}{2}=-1$

$d_2=a_3-a_2=-\frac{5}{2}+\frac{3}{2}=-1$

$d_1=d_2=-1$

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

Hence, the sequence is an arithmetic.

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

$a_n=-\frac{1}{2}+(n-1)(-1)=-\frac{1}{2}-n+1=\frac{1}{2}-n$ for $n\geq 1$