Question

use inductive reasoning to predict the next line in this sequence of computations. then use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct.

\\
\

$$\begin{aligned} 9 \\cdot 3 + 5 &= 32 \\\\ 99 \\cdot 3 + 5 &= 302 \\\\ 999 \\cdot 3 + 5 &= 3002 \\\\ 9999 \\cdot 3 + 5 &= 30002 \\end{aligned}$$

\\

make a conjecture by predicting the correct numbers in the line below.

\\ 99999 \cdot 3 + 5 = 300002 \\

is the conjecture correct?
a. yes
b. no

Explanation:

Analyze the pattern of the computations

$$
LATEXBLOCK0
$$

Predict the next line (conjecture)

$$ 99999 \cdot 3 + 5 = 300002 $$

Verify the conjecture arithmetically

$$
LATEXBLOCK1
$$

Answer:

Question 1

The predicted next line is:

$$99999 \cdot 3 + 5 = 300002$$

Question 2

• A. Yes (Correct answer)
• B. No