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 27. (simplify your answer.) the next term in the sequence, $a_6$, is $\square$. (simplify your answer.)

Explanation:

Step1: Identify the common difference

In an arithmetic sequence, the common difference \(d\) is constant. For the sequence \(15, 18, 21, 24, \dots\), we calculate the difference between consecutive terms: \(18 - 15 = 3\), \(21 - 18 = 3\), \(24 - 21 = 3\). So, the common difference \(d = 3\).

Step2: Find the sixth term (\(a_6\))

We know that in an arithmetic sequence, the \(n\)-th term is given by \(a_n = a_1 + (n - 1)d\), where \(a_1\) is the first term, \(d\) is the common difference, and \(n\) is the term number. We already found that \(a_5 = 27\) (since \(a_5=a_4 + d=24 + 3 = 27\)). To find \(a_6\), we add the common difference to \(a_5\): \(a_6=a_5 + d=27+3 = 30\).

Answer:

30