Question

Observe the following pattern of sums of odd numbers

1 = 1 = 1³

3 + 5 = 8 = 2³

7 + 9 + 11 = 27 = 3³

13 + 15 17 + 19 = 64 = 4³

21 + 23 + 25 + 27 + 29 = 125 = 5³

Think on this pattern tell : How many consecutive odd numbers will be needed to get the sum of 10³?

Answer 1

From above pattern, we sec cube of 1 consists is 1 odd number

Cube of 2 Consists 2 odd numbers 3, 5

Cube of 3 Consists 3 odd numbers 7, 9, 11 

Cube of 4 Consists 4 odd numbers 13, 15, 17, 19 

_____________________________ 

∴ Cube of 10 consists 10 consecutive odd numbers.