Question

While trying to express $7^3$ as the sum of consecutive odd numbers, after finding the middle number(s) what is the next step?

• A. Find the odd numbers which give a sum of 49.
• B. Find 7 consecutive odd numbers after 49.
• C. Find 3 consecutive odd numbers on either side of 49.
• D. None of these

Answer 1

The correct option is C Find 3 consecutive odd numbers on either side of 49.

After dividing $7^3$ by 7, if the quotient is an odd number then the quotient (49) is the middle number. If the quotient is an even number, the numbers on either side of the quotient are the middle numbers. After the middle number(s) is found, we need to find $7-1=6$ more odd numbers.
The next step is to find 3 immediate odd numbers on either side of the middle number. The numbers are- 43, 45, 47, 49, 51, 53, 55.