Question

16 a student exercises 5 minutes the first day, 12 minutes the second day, and 19 minutes the third day. this situation models an arith day 15, how many minutes does the student exercise? a 98 minutes b 75 minutes c 110 minutes d 103 minutes

Explanation:

Step1: Identify the sequence type

The exercise times are 5, 12, 19,... This is an arithmetic sequence where the first term \(a_1 = 5\) and the common difference \(d=12 - 5=7\).

Step2: Use the arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n=a_1+(n - 1)d\). For \(n = 15\), \(a_1=5\), \(d = 7\).

Substitute the values: \(a_{15}=5+(15 - 1)\times7\)

Step3: Calculate the value

First, calculate \((15 - 1)\times7=14\times7 = 98\). Then, \(a_{15}=5 + 98=103\).

Answer:

D. 103 minutes