Questions: Find the indicated term for the arithmetic sequence with first term, (a1), and common difference, (d). Find (a9), when (a1=-3, d=5). (a9=)

Transcript text: Find the indicated term for the arithmetic sequence with first term, $a_{1}$, and common difference, $d$. Find $a_{9}$, when $a_{1}=-3, d=5$. \[ a_{9}= \]

Solution

Solution Steps

To find the indicated term in an arithmetic sequence, we use the formula for the nth term: $ a_n = a_1 + (n-1) \times d $. Here, $ a_1 $ is the first term, $ d $ is the common difference, and $ n $ is the term number we want to find. For this problem, we need to find the 9th term ($ a_9 $) given that $ a_1 = -3 $ and $ d = 5 $.

Step 1: Identify the Given Values

We are given the first term of the arithmetic sequence $ a_1 = -3 $ and the common difference $ d = 5 $. We need to find the 9th term of the sequence, denoted as $ a_9 $.

Step 2: Apply the Formula for the nth Term

The formula for the nth term of an arithmetic sequence is given by: \[ a_n = a_1 + (n - 1) \times d \] Substituting the known values into the formula for $ n = 9 $: \[ a_9 = -3 + (9 - 1) \times 5 \]

Step 3: Perform the Calculation

Calculating the expression: \[ a_9 = -3 + 8 \times 5 \] \[ a_9 = -3 + 40 \] \[ a_9 = 37 \]