if this pattern continues, how many squares will be in the 10th figure?\na. 14\nb. 20\nc. 26\nd. 29\ne. 32

Explanation:

Step1: Analyze the pattern

Figure 1 has 5 squares ($3 + 2$), Figure 2 has 8 squares ($6+ 2$), Figure 3 has 11 squares ($9 + 2$). The number of squares in the non - additional part forms an arithmetic sequence with first term $a_1 = 3$ and common difference $d = 3$, and there are always 2 additional squares.

Step2: Find the formula for the number of squares in the $n$th figure

The formula for the $n$th term of an arithmetic sequence is $a_n=a_1+(n - 1)d$. Here, the number of squares in the non - additional part is $3+(n - 1)\times3=3n$. The total number of squares $S_n$ in the $n$th figure is $S_n=3n + 2$.

Step3: Calculate the number of squares in the 10th figure

Substitute $n = 10$ into the formula $S_n=3n + 2$. So $S_{10}=3\times10+ 2=30 + 2=32$.

Answer:

E. 32