Question 38 of 44intermediate🔧 ApplyShort Answer3 marks

Find the sum of the odd numbers between 0 and 50.

Correct Answer

The sum of the odd numbers between 0 and 50 is 625.

Exercise: EXERCISE 5.3 | Q: 14 | (Page Page 21)
For More Understanding

Explanation

This question asks students to find the sum of odd numbers between 0 and 50. The odd numbers form an arithmetic progression: 1, 3, 5, 7, ..., 49. Students need to identify the first term (a = 1), common difference (d = 2), and last term (l = 49). Using the formula for nth term, they find n = 25 terms. Then applying the sum formula Sₙ = n/2 × (a + l), they calculate S₂₅ = 25/2×502 \times 50 = 625.

Solution Steps

  1. Step 1: Identify the AP - Odd numbers between 0 and 50: 1, 3, 5, 7, ..., 49

  2. Step 2: Find parameters - First term (a) = 1, common difference (d) = 2, last term (l) = 49

  3. Step 3: Find number of terms using aₙ = a + (n-1)d: 49 = 1 + (n-1) × 2, solving gives n = 25

  4. Step 4: Apply sum formula Sₙ = n/2 × (a + l): S₂₅ = 25/2 × (1 + 49) = 25/2×502 \times 50 = 625

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