Question

What is the \[{{n}^{th}}\] term of the sequence 1, 4, 9, 16, 25?

Answer 1

Hint: In this problem, we have to find the \[{{n}^{th}}\] term of the sequence 1, 4, 9, 16, 25. We can see that the given terms in the sequence are the squared terms of natural numbers. We can now say that the \[{{n}^{th}}\] will also be the squared term. We can now find it from the following steps.

Complete step-by-step answer:
Here we have to find the \[{{n}^{th}}\] term of the sequence 1, 4, 9, 16, 25.
We can see that the terms in the sequence are the squared terms, where the first term is,
\[\Rightarrow 1=1\times 1\]
We can now write the second term,
\[\Rightarrow 4=2\times 2\]
The third term is the squared term of 3,
\[\Rightarrow 9=3\times 3\]
The fourth term is the squared term of 4,
\[\Rightarrow 16=4\times 4\]
We can see that the last term can be written as,
\[\Rightarrow 25=5\times 5\]
Similarly, we can write the \[{{n}^{th}}\] term as,
\[\Rightarrow n\times n={{n}^{2}}\]
Therefore, the \[{{n}^{th}}\] term of the sequence 1, 4, 9, 16, 25 is \[{{n}^{2}}\].

Note: Students should know that the given sequence in this problem has no common difference, so we cannot use any formulas to find the \[{{n}^{th}}\] term. For these types of problems, we have to find the \[{{n}^{th}}\] term by solving logically as here we can see the terms are the squared terms so the \[{{n}^{th}}\] term will also be the square of itself, in case of having any negative terms, we will get a different \[{{n}^{th}}\] term.