Page 31 - Concepts of Reasoning-8

Worksheet-3.2

Patterns in Square Numbers

1. The following is the list of triangular numbers. Use the property of squares related to the
triangular numbers and fill in the empty boxes. Write the property used in the blank
provided at the end. One is done for you.

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300,
325, 351, 378, 406 171 + 190 = 361 = 19 2
a. 45 + 55 = __________ = __________

b. 105 + 120 = __________ = __________
c. 153 + 171 = __________ = __________

d. 253 + 276 = __________ = __________
e. 351 + 378 = __________ = __________

Property : ______________________________________________________________________

_______________________________________________________________________________

2. Match the following addition expressions with their values without doing the actual
addition.Write the property used in the blank provided below :

a. 1+ 3 + 5 + 7 i. 64
b. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 ii. 196

c. 1 + 3 + 5 iii. 100

d. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 iv. 9
e. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 v. 16

Property : ______________________________________________________________________
_______________________________________________________________________________

3. Pick up the numbers from the box given below and form five different sets of Pythagorean triplets
matching the criteria given for each of them.

3 10 48 80 12 20 4 8 26 50 18 35 17 50 63

a. Smallest member is 6; Pythagorean triplet : ____________
b. Largest member is 5; Pythagorean triplet : ____________
c. Middle member is 24; Pythagorean triplet : ____________

d. Smallest member is 14; Pythagorean triplet : ____________
e. Largest member is 82; Pythagorean triplet : ____________

31 Reasoning - 8