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NCERT Solutions for Class 5th Maths Chapter 4 Sums of Consecutive Numbers — In-text Questions

Book page 46 Updated on2026-09-19

Q1.
Notice how the sums of 3, 4, and 5 consecutive numbers are related to the numbers being added. Use your understanding to find the following sums without adding the numbers directly. (a) 67 + 68 + 69 (b) 24 + 25 + 26 + 27 (c) 48 + 49 + 50 + 51 + 52 (d) 237 + 238 + 239 + 240 + 241 + 242
Answer

The red arrows in the book pair the outside numbers together. That is the whole secret.

67 + 68 + 69 67 + 69 = 136 136 + 68 = 204 = 3 × 68 = 204
Two outside numbers make twice the middle one, so three consecutive numbers make three times the middle one.

Two rules to use

  • Odd count (3 numbers, 5 numbers): sum = count × middle number.
  • Even count (4 numbers, 6 numbers): pair the outside numbers. Every pair adds to the same total, so sum = (count ÷ 2) × (first + last).

(a) 67 + 68 + 69 = 204

  1. Three numbers, so the middle one is 68.
  2. Sum = 3 × 68.
  3. 3 × 68 = 204.

(b) 24 + 25 + 26 + 27 = 102

  1. Four numbers, so make 2 pairs.
  2. 24 + 27 = 51 and 25 + 26 = 51 — both pairs give the same total.
  3. Sum = 2 × 51 = 102.

(c) 48 + 49 + 50 + 51 + 52 = 250

  1. Five numbers, so the middle one is 50.
  2. Sum = 5 × 50.
  3. 5 × 50 = 250.

(d) 237 + 238 + 239 + 240 + 241 + 242 = 1,437

  1. Six numbers, so make 3 pairs.
  2. 237 + 242 = 479, 238 + 241 = 479, 239 + 240 = 479.
  3. Sum = 3 × 479.
  4. 3 × 479 = 1,437.
Why the pairs are always equal: Move one step in from the left and the number goes up by 1. Move one step in from the right and the number goes down by 1. The gain and the loss cancel out, so every pair keeps the same total.
Check it yourself: Add (b) the long way — 24 + 25 = 49, 49 + 26 = 75, 75 + 27 = 102 ✓ The shortcut gave the same answer far faster.
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