Rachel is placing playing cards on a table by following these steps. Step 1: First she places one card in the middle of the table. Step 2: Next she adds one more card directly to the left, to the right, above, and below the first card. Step 3: Next she adds one more card directly to the left, to the right, above, and below the cards that were already on the table. The cards form the pattern shown. The figure shows 9 cards. One card is placed in the middle. 2 cards are placed above it, 2 cards are placed below, 2 cards are placed to the right and 2 cards are placed to the left. If Rachel continues the same pattern, how many cards will be on the table after Rachel completes Step 4? Write the first 6 terms of the sequence that represents the total number of cards on the table after each step. Describe the pattern in the sequence.
Meow, I'm very confused please help me.
Try doing the pattern 4 times.
its hard but if you need a study buddy my number is +17629946200 hmu ill be your study buddy! x
Well, don't worry! I'm here to help you figure it out.
To find out how many cards will be on the table after Rachel completes Step 4, let's first look at the pattern and figure out the number of cards at each step.
Step 1: 1 card
Step 2: 1 + 4 = 5 cards
Now let's analyze the pattern to see how the number of cards increases at each step.
In Step 1, there is only 1 card. In Step 2, Rachel adds 4 more cards around the initial card, which gives a total of 5 cards.
For Step 3, Rachel adds another set of cards around the existing ones. This means that for each card in Step 2, she adds 4 more cards. So the number of cards at Step 3 would be 5 (cards from Step 2) multiplied by 4, plus the 1 card from Step 1. That gives us a total of 21 cards.
Now, for Step 4, we can use the same logic. Rachel will take the 21 cards from Step 3 and add 4 more cards for each of those cards. So the number of cards at Step 4 would be 21 multiplied by 4, plus the 5 cards from Step 2 and 1 card from Step 1.
That gives us a total of 85 cards for Step 4.
To summarize the sequence of the total number of cards after each step:
Step 1: 1
Step 2: 5
Step 3: 21
Step 4: 85
The pattern appears to be increasing by multiplying the previous step's total by 4 and adding the number of cards from the second step.
I hope that helps! Let me know if you have any more questions. And remember, don't let numbers get you all tangled up like a ball of yarn. Meow!
No worries! Let's break it down step by step.
Step 1: Rachel places one card in the middle of the table.
Total cards on the table after Step 1: 1
Step 2: Rachel adds one card directly to the left, right, above, and below the first card.
Total cards on the table after Step 2: 1 + 4 = 5
Step 3: Rachel adds one card directly to the left, right, above, and below the cards that were already on the table.
Total cards on the table after Step 3: 5 + 4 = 9
To find out how many cards will be on the table after Step 4, we need to continue the same pattern.
Step 4: Rachel will add one card directly to the left, right, above, and below the cards that were already on the table (in this case, 9 cards).
Total cards on the table after Step 4: 9 + 4 = 13
To write the first 6 terms of the sequence that represents the total number of cards on the table after each step, we have:
Step 1: 1 card
Step 2: 5 cards
Step 3: 9 cards
Step 4: 13 cards
To describe the pattern in the sequence, we can see that the number of cards is increasing by 4 after each step. So, we can say that the sequence follows an arithmetic pattern with a common difference of 4.
To find out how many cards will be on the table after Rachel completes Step 4, we need to understand the pattern and sequence that is being followed.
Step 1: 1 card in the middle.
Step 2: 1 + 4 = 5 cards.
Step 3: 5 + 8 = 13 cards.
Based on the given information, we can observe the following pattern:
- In Step 2, 4 cards are added to the original card.
- In Step 3, 8 cards are added to the previous total.
So, if Rachel continues the same pattern, in Step 4, 13 cards will be added to the previous total (13), making a total of 13 + 13 = 26 cards on the table after Rachel completes Step 4.
To write the first 6 terms of the sequence that represents the total number of cards on the table after each step, we can list them as follows:
Step 1: 1
Step 2: 5
Step 3: 13
Step 4: 26
Step 5: 49
Step 6: 81
The pattern in the sequence can be described as follows:
- Each step increases the total number of cards by adding twice the number of cards added in the previous step.
- In other words, the number of cards added in each step follows a pattern of doubling.
I hope this helps!