Q50. - Algebra 2

Question

Refer to the first three arrays of numbers below.

Write an equation representing the nth number in this pattern?

Step-by-Step Solution

Answer

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

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 $4n-3$