Question

Is the sequence 5,9,15———-an arithmetic?

Answer 1

5, 9, 15,....is not an arithmetic sequence.

Explanation:

Arithmetic sequence is a sequence in which difference between the consecutive terms is constant.

Example: 0 , 5, 10, 15, 20 is an arithmetic sequence with common difference of 5 between the terms.

Consider the given sequence,

5, 9, 15,....

Here,
`a_1=5\\\\a_2=9\\\\a_3=15`

We first find the difference between the terms,

`a_2-a_1=9-5=4`

`a_3-a_2=15-9=6`

Since the difference is not constant .

So,it is not an arithmetic sequence.

Answer 2

No, the given sequence is not arithmetic.

Explanation:

The given sequence is

`5,9,15,....`

The first term is 5.

A sequence is an arithmetic, if the difference between any two consecutive terms are same.

The difference between terms are

`d_1=9-5=4`

`d_2=15-9=6`

`d_1\\eq d_2`

Since the difference between consecutive terms are not same, therefore given sequence is not arithmetic.