Answer:
We conclude that the sequence is NEITHER geometrc nor arithmetic.
Step-by-step explanation:
Given the sequence
[tex]2,6,10,16,...[/tex]
As we know that
An arithmetic sequence has a constant difference d and is defined by:
[tex]a_n=a_1+\left(n-1\right)d[/tex]
Computing the differences between all adjacent terms:
[tex]6-2=4,\:\quad \:10-6=4,\:\quad \:16-10=6[/tex]
The difference is not constant
Hence, the sequence is NOT arithmetic.
NOW, let's check whether is a geometric sequence or not
A geometric sequece has a constant common ration r and is defined by:
[tex]a_n=a_0\cdot r^{n-1}[/tex]
Computing the common ratios between all adjacent terms:
[tex]\frac{6}{2}=3,\:\quad \frac{10}{6}=1.66666\dots ,\:\quad \frac{16}{10}=1.6[/tex]
The ratio is not constant
Hence, the sequence is NOT geometric.
Therefore, we conclude that the sequence is NEITHER geometrc nor arithmetic.
