Question

Select the answer that contains all of the expressions that give the number of small squares in Step n. Step 1 Step 2 Step 3 A.n²+1 B. n(n + 1) C. n²+n D. n+ n+ 1 В. С . A.B.C. B.CD AD

Answer 1

The expression that gives the number of small squares in Step n is n²+n.

Step-by-step explanation:

The expression that gives the number of small squares in Step n is n²+n.

Here's why:

Step 1 has 1 small square, which is 1².

In Step 2, we can count the number of small squares as 2²+2 = 4+2 = 6.

In Step 3, the number of small squares is 3²+3 = 9+3 = 12.

So, the expression n²+n gives the correct number of small squares in each step.

Answer 2

In the given figure:

step 1 has 2 blocks

step 2 has 6 blocks

step 3 has 12 blocks

1)

`\begin{gathered} n^2+1 \\ \text{for step1, n =1} \\ 1^2+1=2 \\ \text{for step2, n=2} \\ 2^2+1=5 \\ \text{ but in step 2, there are 6 blocks} \\ \text{ So, expression: n}^2+1\text{ is not valid} \end{gathered}`

2) n( n + 1 )

`\begin{gathered} \text{ for step 1, n=1} \\ n(n+1) \\ 1(1+1)_{} \\ 1(2)=2 \\ \text{Step 1 has two blocks} \\ \text{for step 2, n=2} \\ n(n+1)=2(2+1) \\ n(n+1)=2(3) \\ n(n+1)=6 \\ \text{step 2 has 6 blocks} \\ \text{for step 3, }n=3 \\ n(n+1)=3(3+1) \\ n(n+1)=3(4) \\ n(n+1)=12 \\ \text{ step 3 has 12 blocks} \\ \text{Thus, expression : n(n+1) is valid} \end{gathered}`

n( n + 1 ) is valid

3)

`n^2+n`

Since the expression can also write as:

`n^2+n=n(n+1)`

Thus, n^2 +n is also valid

4)

`\begin{gathered} n+n+1 \\ \text{for step 1, n = 1} \\ 1+1+1=3 \\ \text{but step 1 has 2 block not 3,} \\ \text{thus, the expression is not valid} \end{gathered}`

n + n + 1 is not valid

Answer :

b) n( n + 1 )

c) n^2 + n