Question

a. find the common difference of the arithmetic sequence. 6, 12, 18, 24, ... part b b. find the next three terms.

Explanation:

Part A: Step1: Recall common difference formula

The common difference \( d \) of an arithmetic sequence is \( d = a_{n + 1}-a_{n} \).

Part A: Step2: Calculate common difference

Take \( a_1 = 6 \), \( a_2 = 12 \), then \( d=a_2 - a_1=12 - 6 = 6 \).
Check with \( a_3 = 18 \), \( d=a_3 - a_2=18 - 12 = 6 \), and \( a_4 = 24 \), \( d=a_4 - a_3=24 - 18 = 6 \). So common difference is 6.

Part B: Step1: Recall arithmetic sequence term formula

The \( n \)-th term of an arithmetic sequence is \( a_n=a_1+(n - 1)d \), and to find next terms, we can also add \( d \) to the last known term.

Part B: Step2: Find next three terms

Last known term is 24.
First next term: \( 24 + 6 = 30 \)
Second next term: \( 30 + 6 = 36 \)
Third next term: \( 36 + 6 = 42 \)

Answer:

Part A: The common difference is \( \boldsymbol{6} \).
Part B: The next three terms are \( \boldsymbol{30} \), \( \boldsymbol{36} \), \( \boldsymbol{42} \).