Question 37 of 44beginner🔧 ApplyShort Answer3 marks

Find the sum of the first 15 multiples of 8.

Correct Answer

The first 15 multiples of 8 are: 8, 16, 24, 32, ..., 120. This forms an Arithmetic Progression (AP) with first term (a) = 8, common difference (d) = 8, number of terms (n) = 15, and last term (l) = 15×815 \times 8 = 120. Using the formula for sum of first n terms of an AP: S_n = n/2(a + l)

Calculation: S_15 = 15/2 × (8 + 120) S_15 = 15/2×1282 \times 128 S_15 = 15×6415 \times 64 S_15 = 960

Therefore, the sum of the first 15 multiples of 8 is 960.

Exercise: EXERCISE 5.3 | Q: 13 | (Page Page 21)
For More Understanding

Explanation

This question tests understanding of Arithmetic Progressions. The multiples of 8 form an AP with a = 8, d = 8. The 15th multiple is 120. Using the sum formula S_n = n/2(a + l) from Example 14 in the textbook, students calculate S_15 = 15/2(8 + 120) = 960.

Solution Steps

  1. Step 1: Identify that multiples of 8 form an AP with a = 8, d = 8, n = 15

  2. Step 2: Find the last term: l = 15×815 \times 8 = 120

  3. Step 3: Apply sum formula: S_n = n/2(a + l)

  4. Step 4: Calculate: S_15 = 15/2 × (8 + 120) = 15/2×1282 \times 128 = 15×6415 \times 64 = 960

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