Question

Refer to the first three arrays of numbers below.

Write an equation representing the nth number in this pattern?

Short answer

The equation representing the nth number in the pattern is$4n-3$ .

Step-by-step solution

Step 1. Given Information.

Given pattern is:

Step 2. Calculation.

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

Here the first term is $a_1=1$

The difference between the first two terms is $5-1=4$

The difference between the next two terms is $9-5=4$

Hence, the common difference is $d=4$

Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_n=1+(n-1)\left(4\right)\\ a_n=1+4n-4\\ a_n=4n-3\end{array}$

Step 3. Conclusion.

Hence, the equation representing the nth number in the pattern is $4n-3$