Question

Choose the correct option for the first and last numbers of $6^3$, as a sum of consecutive odd integers from the following.

• A. 33. 43
• B. 31, 41
• C. 29, 39
• D. 35, 45

Answer 1

The correct option is B 31, 41

The cube of a number can be wriiten as the sum of consecutive odd integers.
$1^3=1$
$2^3=3+5$
$3^3=7+9+11$
$4^3=13+15+17+19$
$5^3=21+23+25+27+29$
Similarly,
$6^3=31+33+35+37+39+41$

Thus, the first odd integer will be 31 and the last odd integer will be 41.