Math Problem Statement
Find the sum of the first 47 terms of the following series, to the nearest integer. 12, comma, 16, comma, 20, comma, point, point, . 12,16,20,...
Solution
The given sequence is an arithmetic progression (AP) where the first term and the common difference .
The formula for the sum of the first terms of an arithmetic progression is:
Here:
- (number of terms),
- (first term),
- (common difference).
Substituting these values into the formula:
Let's calculate the sum.
Thus, the sum of the first 47 terms of the series is .
Would you like more details or explanations? Here are some related questions:
- How do you find the general term of an arithmetic series?
- What is the difference between arithmetic and geometric sequences?
- How do you derive the formula for the sum of an arithmetic series?
- How can you find the sum if you know only the first and last term?
- What are other applications of arithmetic progressions in real life?
Tip: Always check if a sequence follows a pattern like arithmetic or geometric before applying formulas.
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Math Problem Analysis
Mathematical Concepts
Arithmetic Progression
Sequences and Series
Formulas
Sum of Arithmetic Progression: S_n = (n/2) × (2a + (n - 1) × d)
Theorems
Arithmetic Progression Sum Formula
Suitable Grade Level
Grades 9-12
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