Question

Refer to the first three arrays of numbers below.

Is 397 a number in this pattern? Explain.

Short answer

Yes,397 is a number in the pattern and is the100^th term.

Step-by-step solution

Step 1. Given Information.

Given pattern is:

And the nth term is represented by $a_n=4n-3$

Step 2. Calculation.

The n^th term of an arithmetic sequence is given by $a_n=a_1+(n-1)d$.

Here the given term is $a_n=397$

Plugging the values in the formula:

$\begin{array}{l}{a}_n=4n-3\\ 397=4n-3\\ 4n=397+3\\ 4n=400\\ n=100\end{array}$

Since n is natural number, 397 is a number in the pattern.

Step 3. Conclusion.

Hence, 397 is a number in the pattern and is the 100^th term.