Question

5, 16, 27, 38, 49, ...
what is the common difference?
11
what is the value of the first term?
5
write a simplified expression for the right half of the equation that can be used to find the nth term in the sequence.
$a_n = $

Explanation:

Step1: Recall arithmetic sequence formula

The formula for the nth 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: Identify \( a_1 \) and \( d \)

We know \( a_1 = 5 \) (from the second question) and \( d = 11 \) (from the first question).

Step3: Substitute into the formula

Substitute \( a_1 = 5 \) and \( d = 11 \) into the formula:
\[

$$\begin{align*} a_n&= 5+(n - 1)\times11\\ &= 5 + 11n- 11\\ &= 11n-6 \end{align*}$$

\]

Answer:

\( 11n - 6 \)