Question

Decide whether the sequence is artithemetic, geometric or neither 2,6,10,16

Answer 1

We conclude that the sequence is NEITHER geometrc nor arithmetic.

Explanation:

Given the sequence

`2,6,10,16,...`

As we know that

An arithmetic sequence has a constant difference d and is defined by:

`a_n=a_1+\left(n-1\right)d`

Computing the differences between all adjacent terms:

`6-2=4,\:\quad \:10-6=4,\:\quad \:16-10=6`

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:

`a_n=a_0\cdot r^(n-1)`

Computing the common ratios between all adjacent terms:

`(6)/(2)=3,\:\quad (10)/(6)=1.66666\dots ,\:\quad (16)/(10)=1.6`

The ratio is not constant

Hence, the sequence is NOT geometric.

Therefore, we conclude that the sequence is NEITHER geometrc nor arithmetic.