Question

the ancient greeks labeled certain numbers as triangular numbers. the numbers 1, 3, 6, 10, 15, 21, and so on are triangular numbers. complete parts a) through c) below

(images of dot patterns for 1, 3, 6, 10, 15, 21)

a) determine the next two triangular numbers.
1, 3, 6, 10, 15, 21, \square, \square

Explanation:

Step1: Identify pattern of differences

The differences between consecutive triangular numbers increase by 1 each time: $3-1=2$, $6-3=3$, $10-6=4$, $15-10=5$, $21-15=6$.

Step2: Calculate first next number

Add 7 to 21 (since the next difference is 7).
$21 + 7 = 28$

Step3: Calculate second next number

Add 8 to 28 (since the following difference is 8).
$28 + 8 = 36$

Answer:

28, 36