Mathematics Reasoning Long Questions (Question 6)


Question 6:
(a) Complete the following mathematical sentence by writing the symbol > or <.
      (i)                53 ____ 20 is a false statement.
      (ii)             – 3 ____ – 10 is a true statement.

(b) Complete the conclusion in the following argument:
Premise 1 : If  n 1 2 = n , then  4 1 2 = 4 =2. Premise 2 :  n 1 2 = n Conclusion : _____________________
(c) Make a general conclusion by induction for the sequence of numbers 10,
     35, 70, … which follows the following pattern.

10 = 5 (2)2 – 10 
35 = 5 (3)2 – 10
70 = 5 (4)2 – 10
…. = ………..
Solution:
(a)(i) 53   <    20 is a false statement.
(a)(ii)   – 3    >    – 10 is a true statement.

(b)
Conclusion :  4 1 2 = 4 =2

(c) 5 (n + 1)2 – 10, where n = 1, 2, 3, …