Question

find the 23^rd term of the arithmetic sequence whose common difference is d=3 and whose first term is a_1=5.

Explanation:

Step1: Recall the formula for the nth term of an arithmetic sequence.

The formula for the \( n \)-th term of an arithmetic sequence is \( a_n = a_1+(n - 1)d \), where \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the term number.

Step2: Substitute the given values into the formula.

We are given that \( a_1 = 5 \), \( d = 3 \), and \( n = 23 \). Substituting these values into the formula:
\( a_{23}=5+(23 - 1)\times3 \)

Step3: Simplify the expression.

First, calculate \( 23 - 1 = 22 \). Then, multiply \( 22\times3 = 66 \). Finally, add \( 5+66 = 71 \).

Answer:

\( 71 \)