# 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:
$\overline{)\begin{array}{l}\text{Premise 1 : If}{n}^{\frac{1}{2}}=\sqrt{n},\text{then}{4}^{\frac{1}{2}}=\sqrt{4}=2.\\ \text{Premise 2 :}{n}^{\frac{1}{2}}=\sqrt{n}\\ \text{Conclusion : _____________________}\end{array}}$
(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)

$\text{Conclusion :}{4}^{\frac{1}{2}}=\sqrt{4}=2$

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