# 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