Question

1, 3, 6, 10, 15, 21, 28, 36
(b) describe a procedure to determine the next five triangular numbers without drawing the figures. choose the correct answer below.
a. to obtain the 8th triangular number, add 8 to the 7th triangular number. to obtain the 9th triangular number, add 9 to the 8th triangular number, and so on.
b. successively add 8, 10, 12, and 14.
c. add the last two triangular numbers together to get the next one.
d. double the previous triangular number and then subtract half of the previous from that.

Explanation:

Triangular numbers follow a pattern where each number is the sum of the first n positive integers. The recursive rule is that each subsequent triangular number is obtained by adding the next positive integer to the previous triangular number. For example: 1, 1+2=3, 3+3=6, 6+4=10, 10+5=15, etc. This matches the description in option A.

Answer:

A. To obtain the 8th triangular number, add 8 to the 7th triangular number. To obtain the 9th triangular number, add 9 to the 8th triangular number, and so on.