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✅Question : Ramon stacks his lego pieces to create columns with a ladder like pattern. He started with 3 lego pieces on the first column and every succeeding column contains 5 more lego pieces than the previous column. How many lego pieces are needed o be satcked on the 16th column? Is the sequence arithmetic or geometric? What are the given? Formula: Solution and encircle the final answer:
✅Answer :
To determine the number of Lego pieces needed to be stacked on the 16th column, we first need to identify the pattern and whether it’s an arithmetic or geometric sequence.
Ramon starts with 3 Lego pieces in the first column and adds 5 more pieces to each succeeding column. This means the sequence is increasing by a constant difference (5) each time. Therefore, the sequence is arithmetic.
Given:
- First term (a): 3 Lego pieces
- Common difference (d): 5 Lego pieces
- Column number (n): 16
The formula for an arithmetic sequence is:
an=a+(n−1)⋅d
Substituting the given values:
a16=3+(16−1)⋅5
Calculating:
a16=3+15⋅5=3+75=78
So, the number of Lego pieces needed to be stacked on the 16th column is 78.
Encircle the final answer: 78.
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