Problem Statement
What is the sum of all odd numbers between 1 and 100?
Explanation
Odd numbers between 1 and 100 form an arithmetic progression: 1, 3, 5, 7, dot dot dot, 99. We need to find the sum of this AP.
First term a equals 1, common difference d equals 2, last term l equals 99. To find number of terms: l equals a plus open parenthesis n minus 1 close parenthesis d. 99 equals 1 plus open parenthesis n minus 1 close parenthesis times 2. 98 equals open parenthesis n minus 1 close parenthesis times 2. n minus 1 equals 49. n equals 50. Sum of AP equals n divided by 2 times open parenthesis a plus l close parenthesis equals 50 divided by 2 times open parenthesis 1 plus 99 close parenthesis equals 25 times 100 equals 2500. Alternative: Sum of first n odd numbers equals n squared. Here n equals 50, so sum equals 50 squared equals 2500.
Code Solution
SolutionRead Only
// Odd numbers: 1, 3, 5, 7, ..., 99 // AP with a=1, d=2, l=99 // Find number of terms: // l = a + (n-1)d // 99 = 1 + (n-1)×2 // 98 = (n-1)×2 // n-1 = 49 // n = 50 // Sum of AP: // Sum = n/2 × (a + l) // Sum = 50/2 × (1 + 99) // Sum = 25 × 100 // Sum = 2500 // Alternative Formula: // Sum of first n odd numbers = n² // n = 50 // Sum = 50² = 2500
Practice Sets
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