How to decide if a given value is a term of Sequence or not

How to decide whether a given Value is a term of
 Sequence or not

QUESTION: The nth term of a sequence is given by n² – 4.

Is 45 a term in this
sequence?

SOLUTION:

Let us suppose that 45 is
a term of a sequence whose nth term is given by n² – 4

Then

n² – 4 = 45

n² = 45 + 4

n² = 49

Take square root on both
sides, we get

n = 7

As 7 is a whole
number, 

so 45 is a term of a
sequence whose nth term is n² – 4.

Try out this
practice question and share its answer in comment below. Let me see how you do.

The nth term of a sequence is
given by n² + 7.

Is 32 a term in this sequence?

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