Question

identify the sequence below as arithmetic, geometric, or neither. then find the next two terms. 15, 18, 21, 24, ... choose the correct type of sequence below. neither geometric arithmetic the next term in the sequence, ( a_5 ), is ( square ). (simplify your answer)

Explanation:

Step1: Identify the sequence type

An arithmetic sequence has a common difference \( d \) between consecutive terms. Let's check the differences:
\( 18 - 15 = 3 \)
\( 21 - 18 = 3 \)
\( 24 - 21 = 3 \)
Since the common difference \( d = 3 \), it is an arithmetic sequence.

Step2: Find the next term (\( a_5 \))

The formula for the \( n \)-th term of an arithmetic sequence is \( a_n = a_1 + (n - 1)d \), where \( a_1 = 15 \), \( d = 3 \), and \( n = 5 \).
\( a_5 = 15 + (5 - 1) \times 3 \)
\( a_5 = 15 + 4 \times 3 \)
\( a_5 = 15 + 12 \)
\( a_5 = 27 \)

Step3: Find the term after \( a_5 \) (\( a_6 \))

Using the same formula, for \( n = 6 \):
\( a_6 = 15 + (6 - 1) \times 3 \)
\( a_6 = 15 + 5 \times 3 \)
\( a_6 = 15 + 15 \)
\( a_6 = 30 \)

Answer:

The sequence is arithmetic. The next term (\( a_5 \)) is \( 27 \), and the term after that (\( a_6 \)) is \( 30 \). For the question about \( a_5 \), the answer is \( 27 \).