/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 38 Find the sum of the first 50 ter... [FREE SOLUTION] | 91影视

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Chapter 11: Problem 38

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

Short Answer

Expert verified
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 by step solution

01

Identify the first term

The first term of the sequence, denoted as \(a\), is -15.
02

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.
03

Determine the number of terms

The number of terms, denoted as \(n\), is provided as 50 in the problem.
04

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.

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