Question
Download Solution PDFHow many terms will have to be added to get a sum of 10877 in the arithmetic series? 5, 9, 13,...
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF- Formula for Sum of Arithmetic Series: The sum (Sn) of an arithmetic series is given by the formula: Sn = (n/2) * [2a + (n-1)d], where 'n' is the number of terms, 'a' is the first term, and 'd' is the common difference.
- Given Values: In this problem, we are given:
- Sn = 10877 (the sum of the series)
- a = 5 (the first term)
- d = 4 (the common difference)
- Substitution: Substitute the given values into the formula: 10877 = (n/2) * [2*5 + (n-1)*4]
- Simplification: Simplify the equation: 10877 = (n/2) * [10 + 4n - 4] 10877 = (n/2) * (4n + 6) 10877 = n * (2n + 3) 10877 = 2n² + 3n
Last updated on Feb 11, 2025
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