NCERT Book Class 8 Mathematics (Part I) Chapter 5 Number Play

5 NUMBER PLAY

5.1 Is This a Multiple Of?
Sum of Consecutive Numbers
Anshu is exploring sums of consecutive numbers. He has written the
following —

7 =3+4
10 = 1 + 2 + 3 + 4
12 = 3 + 4 + 5
15 = 7 + 8
=4+5+6
=1+2+3+4+5

Now, he is wondering —
• “Can I write every natural number as a sum of consecutive
numbers?”
• “Which numbers can I write as the sum of consecutive numbers in
more than one way?”
• “Ohh, I know all odd numbers can be written as a sum of two
consecutive numbers. Can we write all even numbers as a sum of
consecutive numbers?”
• “Can I write 0 as a sum of consecutive numbers? Maybe I should
use negative numbers.”

Explore these questions and any others that may occur to you. Math
Discuss them with the class. Talk
Take any 4 consecutive numbers. For example, 3, 4, 5, and 6. Place ‘+’ and
‘–’ signs in between the numbers. How many different possibilities exist?
Write all of them.
3+4–5+6
3–4–5–6