Question

How many consecutive odd numbers are required to form ${10}^3$ as their sum?

• A. $10$
• B. $11$
• C. $9$
• D. $20$

Answer 1

The correct option is A $10$

We know,

$1=1=1^3$,
$3+5=8=2^3$,
$7+9+11=27=3^3$,

$13+15+17+19=64=4^3$,

$21+23+25+27+29=125=5^3$,

$31+33+35+37+39+41=216=6^3$,

$43+45+47+49+51+53+55=343=7^3$,

$57+59+61+63+65+67+69+71=512=8^3$,

$73+75+77+79+81+83+85+87+89=729=9^3$,

$91+93+95+97+99+101+103+105+107+109=1000={10}^3$.

$\therefore$ $10$ consecutive odd numbers are required to obtain the sum as ${10}^3$.
Hence, option $A$ is correct.