Question

The 20th term in the triangular numbers 1, 3, 6, 10, 15, 21, ... is

• A. 190
• B. 195
• C. 200
• D. 210

Hint:

Remember triangular number formula: $\frac{n(n+1)}{2}$.

Answer 1

The Correct Option is D

To find the 20th term in the sequence of triangular numbers, we need to understand the formula for the nth triangular number.

Triangular numbers can be defined by the formula:

\(T_n = \frac{n(n+1)}{2}\)

where T_n is the nth triangular number.

We are tasked with finding the 20th triangular number, so we substitute n = 20 into the formula:

\(T_{20} = \frac{20(20+1)}{2}\)

Perform the calculation step-by-step:

• First, calculate \(20 \times 21 = 420\)
• Then, divide the result by 2: \(\frac{420}{2} = 210\)

Thus, the 20th term in the sequence of triangular numbers is 210.

Let us validate the options:

• Option 1: 190 - Incorrect
• Option 2: 195 - Incorrect
• Option 3: 200 - Incorrect
• Option 4: 210 - Correct

Therefore, the correct answer is 210.