**Arithmetic Sequences**### Objective:Find the number of terms in the finite arithmetic sequence.### Problem Statement:Given the finite arithmetic sequence:\[ -3, 0, 3, \ldots, 84 \]### Instructions:Determine the total number of terms in this sequence.### Solution Steps:1. **Identify the First Term (a):** The first term \( a = -3 \).2. **Calculate the Common Difference (d):** The common difference \( d \) is found by subtracting the first term from the second term.\[ d = 0 - (-3) = 3 \]3. **Identify the Last Term (l):** The last term \( l = 84 \).4. **Use the Finite Arithmetic Sequence Formula:**\[ l = a + (n-1)d \]Where: - \( l \) is the last term, - \( a \) is the first term, - \( d \) is the common difference, - \( n \) is the number of terms.Rearranging the formula to solve for \( n \):\[ 84 = -3 + (n-1) \times 3 \]\[ 84 = -3 + 3n - 3 \]\[ 84 = 3n - 6 \]\[ 84 + 6 = 3n \]\[ 90 = 3n \]\[ n = \frac{90}{3} \]\[ n = 30 \]### Conclusion:There are a total of 30 terms in the given finite arithmetic sequence.

Name: **Arithmetic Sequences**### Objective:Find the number of terms in the
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: **Arithmetic Sequences**### Objective:Find the number of terms in the finite arithmetic sequence.### Problem Statement:Given the finite arithmetic sequence:\[ -3, 0, 3, \ldots, 84 \]### Instructions:Determine the total number of terms in this sequen