Question

The following patterns are made of small squares.write an expression for the number of small squares in pattern n

Answer 1

Answer:

$(n+2)^2+6$

Step-by-step explanation:

The picture of the question in the attached figure

we know that

In the pattern 1 there are

$small\ squares=(3^2+6)=15$

In the pattern 2 there are

$small\ squares=(4^2+6)=22$

In the pattern 3 there are

$small\ squares=(5^2+6)=31$

we can write the expression in the form

$(n+a)^2+b$

where

$a=2\\b=6$

substitute

$(n+2)^2+6$

Answer 2

An expression for the number of small squares in pattern n is $(n+2)^{2}+6$ .

In the pattern 1:

3 + (3 x 3) + 3 = 15

Number of small squares = 15

In the pattern 2:

3 + (4 x 4) + 3 = 22

Number of small squares = 22

In the pattern 3:

3 + (5 x 5) + 3 =31

Number of small squares = 31

In the pattern n:

$3+(n+2)^{2} +3$

Simplify:

$=(n+2)^{2}+6$

Therefore, an expression for the number of small squares in pattern n is $(n+2)^{2}+6$ .

For more information:

https://brainly.com/question/8912117