Is a number (term) in a sequence?

If you are asked in an exam is a certain number in a sequence

Set the Expression = To the Value 

If the answer is a whole number then, yes, it is a number in the sequence.

Example 1

The `n^(th)` term of a sequence is `2n^2`

Is 400 a term (number) in the sequence?

So set the expression `=` to the value

  `2n^2=400`

therefore  `n^2=400/2=200`

`n=sqrt200`

`n=14.14`  to 2D.P.

The answer has decimal places, it is not a whole number. So the answer is no the number 400 is not in the sequence.

Example 2

The `n^(th)` term of a sequence is `3n+5`

Is 110 a term (number) in the sequence?

So set the expression `=` to the value

    `3n+5=110`

therefore   `3n=110-5=105`

`n=105/3=35`

The answer is a whole number so yes, 110 is a term or number in the sequence `3n+5`