Bookwork code: 4C Aurora is making a sequence of patterns using beads and sticks Her first pattern is made up of 5 beads and 4 sticks. She adds the same number of beads and the same number of sticks each time. a) How many beads are there in the 4^th pattern? b) How many sticks are there in the 4^th pattern? Calculator not allowed

## Step1:In this problem Aurora is creating a pattern with adding a certain number of beads and sticks continuously with each new pattern. The first pattern consists of 5 beads and 4 sticks. The number increases with the same number for each new pattern.## Step2:Theoretically, in the ith pattern, the number of beads will be the number of beads in the first pattern plus the product of the number of beads added each time (which is equals to the number of sticks added as per problem) and . Let's denote it by .\### \(B_i = (5)_{\text{initial number}} + \left(4\right)_{\text{difference between patterns each time}} * (i - 1)\)## Step3:Following the formula, let's compute the number of beads ( ) in the 4th pattern:\## \(B_4 = 5 + 4 * \left(4 - 1\right)\) ## Step4: In analogy to computation in step 2, we can also create a formula ( ) for finding the number of sticks in number ith pattern:\### \(S_i = (4)_{\text{initial number}} + \left(4\right)_{\text{difference between patterns each time}} * (i - 1)\)## Step5:Following the formula, let's compute the number of sticks ( ) in the 4th pattern:\## \(S_4 = 4 + 4 * \left(4 - 1\right) \)