Question

evaluate each expression if $a = 2$ and $b = 8$.

1. $3a + 1$
2. $\frac{24}{b}$

describe the relationship between the terms in the arithmetic sequence. then write the next three terms in each sequence.

1. $4, 9, 14, 19, \dots$
2. $0, 14, 28, 42, \dots$

Explanation:

Problem 1: Evaluate \( 3a + 1 \) when \( a = 2 \)

Step 1: Substitute \( a = 2 \) into the expression

Substitute \( a = 2 \) into \( 3a + 1 \), we get \( 3\times2 + 1 \).

Step 2: Calculate the result

First, calculate \( 3\times2 = 6 \), then \( 6 + 1 = 7 \).

Step 1: Substitute \( b = 8 \) into the expression

Substitute \( b = 8 \) into \( \frac{24}{b} \), we get \( \frac{24}{8} \).

Step 2: Calculate the result

\( \frac{24}{8}=3 \).

Step 1: Find the common difference

Calculate the difference between consecutive terms: \( 9 - 4 = 5 \), \( 14 - 9 = 5 \), \( 19 - 14 = 5 \). So the common difference \( d = 5 \).

Step 2: Find the next three terms

• The fifth term: \( 19 + 5 = 24 \)
• The sixth term: \( 24 + 5 = 29 \)
• The seventh term: \( 29 + 5 = 34 \)

Answer:

\( 7 \)

Problem 2: Evaluate \( \frac{24}{b} \) when \( b = 8 \)