Questions: An arithmetic sequence is given below. 15,21,27,33, ... Write an explicit formula for the nth term an. an=

Transcript text: An arithmetic sequence is given below. \[ 15,21,27,33, \ldots \] Write an explicit formula for the $n^{\text {th }}$ term $a_{n}$. \[ a_{n}= \]

Solution

Solution Steps

Step 1: Identify the First Term and Common Difference

The first term of the arithmetic sequence is given by: \[ a_1 = 15 \] The common difference $d$ can be calculated as: \[ d = 21 - 15 = 6 \]

Step 2: Write the Explicit Formula

The explicit formula for the $n^{\text{th}}$ term of an arithmetic sequence is given by: \[ a_n = a_1 + (n - 1) \cdot d \] Substituting the values of $a_1$ and $d$: \[ a_n = 15 + (n - 1) \cdot 6 \]

Step 3: Calculate the 5th Term

To find the 5th term ($n = 5$): \[ a_5 = 15 + (5 - 1) \cdot 6 \] Calculating this gives: \[ a_5 = 15 + 4 \cdot 6 = 15 + 24 = 39 \]