GATE Civil 2024 Set 2 | GA Question: 4

Question

If the sum of the first $20$ consecutive positive odd numbers is divided by $20^{2}$, the result is

• A. $1$
• B. $20$
• C. $2$
• D. $1 / 2$

Answer 1

Sum of first n positive consecutive odd numbers is $n^2$.

1 + 3 + 5 (3 consecutive odd numbers) ➡ Sum = $3^2 = 9$

1 + 3 + 5 + 7 (4 consecutive odd numbers) ➡ Sum = $4^2 = 16$

Similarly, 20 consecuive odd numbers sum = $20^2 = 400$

So, if the first 20 consecutive positive odd numbers is divided by $20^2$, answer would be $\frac{20^2}{20^2}$ = 1

 

Comments

nicely explained.