Question

If 351 is a triangular number, enter the number corresponding to which one it is.

a) 25
b) 26
c) 27
d) 28

Answer 1

351 is the 26th triangular number, which corresponds to option (b) 26. We arrived at this answer by solving the equation n(n + 1)/2 = 351 for n and finding that n = 26.

Step-by-step explanation:

The student has asked to identify which numbered triangular number corresponds to 351. A triangular number or triangle number is the number of dots in an equilateral triangle evenly filled with dots. The formula for the nth triangular number is n(n + 1)/2.

To find out the position of the triangular number 351, we can set up the equation n(n + 1)/2 = 351 and solve for n.

1. First, multiply both sides of the equation by 2 to get rid of the fraction:
   n(n + 1) = 702.
2. Next, look for a pair of consecutive integers that when multiplied give you 702. After some trial and error or by factoring, we can find that 26 and 27 are those numbers, as 26 * 27 = 702.
3. Therefore, since 26 is our n, we conclude that 351 is the 26th triangular number.

This corresponds to option (b) 26.