Determine whether the following sequence is arithmetic, geometric, or neither. 1, 2, 2, 3, ... arithmetic geometric neither

Question

asked Feb 24, 2019 138k views

2 Answers

Liska Liskor · Answer 1 · 2019-03-02T15:28:21+0000

Answer: neither

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=(a_2)/(a_1)=(a_3)/(a_2)=......=(a_n)/(a_(n-1))}

The given sequence = 1, 2, 2, 3, ...

Here ,
$2-1\\eq2-2$ , so difference between two consecutive terms is not equal.

⇒ Its not an Arithmetic sequence.

Also ,
$(2)/(1)\\eq(2)/(2)\\eq(3)/(2)$ , so ratio between two consecutive terms is also not equal.

⇒ Its not an Geometric sequence.

Hence, the given sequence is neither arithmetic nor geometric.