Question

Determine whether the following sequence is arithmetic, geometric, or neither.

Answer 1

Answer: neither

Step-by-step explanation:

Consider sequence $a_1 , a_2 , a_3 , .....a_n$, where n acn be any natural number.

This sequence is said to be Arithmetic sequence if the difference between two consecutive terms is equal.

i.e, if it is arithmetic then $d=a_2-a_1=a_3-a_2=...=a_n-a_{n-1}$

This sequence is said to be Geometric sequence if the common ratio between two consecutive terms is equal.

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=......=\dfrac{a_n}{a_{n-1}}}$

The given sequence =  1, 2, 2, 3, ...

Here , $2-1\neq2-2$ , so difference between two consecutive terms is not equal.

⇒ Its not an Arithmetic sequence.

Also , $\dfrac{2}{1}\neq\dfrac{2}{2}\neq\dfrac{3}{2}$, so ratio between two consecutive terms is also not equal.

⇒ Its not an Geometric sequence.

Hence, the given sequence is neither arithmetic nor geometric.

Answer 2

The following sequence shown up top is arithmetic sequence