Question

whats the explicit rule for the sequence 9, 14, 19, 24, ...? a) (a_n = 14 + 5(n - 2)) b) (a_n = 9 + 5(n - 1)) c) (a_n = 24 - 5(n - 1)) d) (a_n = 9 + 5(n - 2)) question 12 (5 points) what are the next 4 terms of the sequence 2, 4, 8, 16, ...? a) 32, 64, 128, 256 b) 24, 32, 40, 48 c) 25, 36, 49, 64

Explanation:

Step1: Identify the type of sequence for the first - part

The sequence 9, 14, 19, 24, … is an arithmetic sequence. The first term \(a_1 = 9\) and the common difference \(d=14 - 9=5\). The explicit formula for an arithmetic sequence is \(a_n=a_1 + d(n - 1)\). Substituting \(a_1 = 9\) and \(d = 5\) into the formula, we get \(a_n=9+5(n - 1)\).

Step2: Identify the type of sequence for the second - part

The sequence 2, 4, 8, 16, … is a geometric sequence with first - term \(a_1 = 2\) and common ratio \(r=\frac{4}{2}=2\). To find the next terms, we multiply the last known term by the common ratio. \(16\times2 = 32\), \(32\times2=64\), \(64\times2 = 128\), \(128\times2=256\).

Answer:

1. B. \(a_n = 9+5(n - 1)\)
2. A. 32, 64, 128, 256