Question

the nth odd number is given by: (a) n + 1 (b) 2n (c) 2n - 1 (d) 2n + 2 the parity of 72 × 113 is: a) odd (b) even (c) both (d) cannot be found

Explanation:

First Question (nth odd number):

Step1: Recall odd number pattern

Odd numbers: 1, 3, 5, 7,... For \( n = 1 \), \( 2(1)-1 = 1 \); \( n = 2 \), \( 2(2)-1 = 3 \); \( n = 3 \), \( 2(3)-1 = 5 \). So formula is \( 2n - 1 \).

Step2: Check options

• (a) \( n + 1 \): For \( n = 1 \), \( 2 \) (even), wrong.
• (b) \( 2n \): Even number, wrong.
• (c) \( 2n - 1 \): Matches odd numbers, correct.
• (d) \( 2n + 2 \): Even, wrong.

Step1: Recall parity rules

Even number \( \times \) any number = even. \( 72 \) is even (divisible by 2).

Step2: Determine product parity

Since \( 72 \) is even, \( 72 \times 113 \) is even.

Answer:

(c) \( 2n - 1 \)

Second Question (parity of \( 72 \times 113 \)):