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NCERT Solutions for Class 5th Maths Chapter 4 Sums of Consecutive Numbers — Sums of Consecutive Numbers

Book page 45 Updated on2026-09-19

Q1.
In each of the boxes above, state whether the sums are even or odd. Explain why this is happening.
Answer

Box of 2 consecutive numbers — every sum is odd. Box of 3 — the sums are odd and even turn by turn. Box of 4 — every sum is even.

BoxSums printedEven or odd
2 consecutive numbers3, 5, 7, 9all odd
3 consecutive numbers6, 9, 12, 15even, odd, even, odd
4 consecutive numbers10, 14, 18, 22all even

Why the box of 2 gives only odd sums.

  1. Two consecutive numbers are always one even and one odd — 3 and 4, or 4 and 5.
  2. The even one splits into pairs completely. The odd one leaves one counter alone.
  3. That single counter has no partner, so the total is odd.

Why the box of 4 gives only even sums.

  1. Four consecutive numbers are two even and two odd — for example 3, 4, 5, 6.
  2. The two even numbers pair off with nothing left over.
  3. Each odd number leaves one counter alone, and those two lonely counters join to make one more pair.
  4. Nothing is left over, so the total is even.

Why the box of 3 keeps changing.

  1. The sum of 3 consecutive numbers is 3 times the middle number: 1 + 2 + 3 = 3 × 2 = 6.
  2. The middle numbers are 2, 3, 4, 5 — even, odd, even, odd, one after the other.
  3. 3 × an even number is even; 3 × an odd number is odd.
  4. So the sums go even, odd, even, odd.
Try This: Write the sums of 5 consecutive numbers starting from 1, 2, 3 and 4. You will get 15, 20, 25, 30 — odd and even turn by turn again, for the same reason as the box of 3.
Q2.
What is the difference between two successive sums in each box? Is it the same throughout?
Answer

Yes, it is the same all the way down each box. The jump equals the count of numbers being added.

BoxSumsJump each time
2 consecutive numbers3 → 5 → 7 → 92
3 consecutive numbers6 → 9 → 12 → 153
4 consecutive numbers10 → 14 → 18 → 224
Why it happens: Look at the box of 4. The first row is 1 + 2 + 3 + 4 and the next row is 2 + 3 + 4 + 5. Every number has slid up by exactly 1. There are 4 numbers, so 4 lots of 1 have been added — the sum grows by 4. Nothing else changes, so the jump is 4 every single time.
1 + 2 + 3 + 4 = 10
2 + 3 + 4 + 5 = 14   (each number 1 bigger, 4 numbers, so +4)
3 + 4 + 5 + 6 = 18   (+4 again)
Q3.
What will be the difference between two successive sums for — (a) 5 consecutive numbers (b) 6 consecutive numbers
Answer

(a) 5    (b) 6

The rule from Q2 is: the jump is the same as how many numbers you are adding.

(a) Five consecutive numbers

  1. 1 + 2 + 3 + 4 + 5 = 15.
  2. 2 + 3 + 4 + 5 + 6 = 20.
  3. The jump is 20 − 15 = 5, because 5 numbers each grew by 1.

(b) Six consecutive numbers

  1. 1 + 2 + 3 + 4 + 5 + 6 = 21.
  2. 2 + 3 + 4 + 5 + 6 + 7 = 27.
  3. The jump is 27 − 21 = 6, because 6 numbers each grew by 1.
Check it yourself: Carry on with 3 + 4 + 5 + 6 + 7 + 8 = 33. And 33 − 27 = 6 ✓ The jump stays 6 for ever.
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