Answer:
n^2+3
Step-by-step explanation:
As we can see in the diagram
1st pattern consists from 1 square 1x1 +3 squares 1x1 each
2nd pattern consists from 1 square 2x2 +3 squares 1x1 each
3-rd pattern consists from 1 square 3x3 +3 squares 1x1 each
4-th pattern consists from 1 square 4x4 + 3 squares 1x1 each
We can to continue :
5-th pattern consists from 1 square 5x5+3 squares 1x1 each
So the nth pattern consists from 1 square nxn+3 squares 1x1 each
Or total amount of 1x1 squares in nth pattern N= n^2+3
The expression for the numbers of squares in the nth pattern of the sequence is [tex]n^{2} +3[/tex].
"The nth term of a sequence is a formula that enables us to find any term in the sequence. We can make a sequence using the nth term by substituting different values for the term number(n) into it."
From the given diagram
We can see that every term is made up with a square which side is n and three small square side is 1.
So,
1st term is 1 × 1 + 3 = 4
2nd term is 2 × 2 + 3 = 4
3rd term is 3 × 3 + 3 = 12
4th term is 4 × 4 + 3 = 19
So, nth term is [tex]n^{2} +3[/tex]
Hence, The expression for the numbers of squares in the nth pattern of the sequence is [tex]n^{2} +3[/tex].
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