Problem 38 - Algebra and Trigonometry

Question

Find the sum of the first 50 terms of the arithmetic sequence: \(-15,-9,-3,3,\)

Step-by-Step Solution

Answer

The sum of the first 50 terms of the given arithmetic sequence is calculated as \(S_{50} = \frac{50}{2} [2(-15) + (50-1) 6]\).

Step 1: Identify the first term

The first term of the sequence, denoted as \(a\), is -15.

Step 2: Identify the common difference

The common difference of the sequence, denoted as \(d\), is found by subtracting the first term from the second term or the second term from the third term, etc. In this case, -9 - (-15) = 6.

Step 3: Determine the number of terms

The number of terms, denoted as \(n\), is provided as 50 in the problem.

Step 4: Apply the mathematical formula

Applying the formula \(S_n = \frac{n}{2} [2a + (n-1) d]\) using the values obtained in previous steps, i.e., \(a\) = -15, \(d\) = 6, and \(n\) = 50, the sum of the first 50 terms, \(S_{50}\), can be calculated.