Question

find the 24th term of the arithmetic sequence whose common difference is d = 2 and whose first term is a1 = 3.

Explanation:

Step1: Recall the formula for the nth term

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

Step2: Identify the values of $a_1$, $n$, and $d$

We are given that $a_1 = 3$, $n = 24$, and $d=2$.

Step3: Substitute the values into the formula

Substitute $a_1 = 3$, $n = 24$, and $d = 2$ into the formula $a_n=a_1+(n - 1)d$.
$a_{24}=3+(24 - 1)\times2$.

Step4: Simplify the expression

First, calculate the value inside the parentheses: $24−1 = 23$.
Then, multiply: $23\times2=46$.
Finally, add: $3 + 46=49$.

Answer:

49