Figure out the value of the 20th Triangular Number

Question

Answer

Calculating the 20th Triangular Number

A triangular number is the sum of consecutive integers starting from 1. The formula for the nth triangular number is:

T_n = 1 + 2 + 3 + ... + n

Finding the 20th Triangular Number

To find the 20th triangular number, we simply plug in n = 20 into the formula:

T₂₀ = 1 + 2 + 3 + ... + 20

We can use the formula for the sum of an arithmetic sequence to simplify the calculation:

S_n = n/2 * (a₁ + a_n)

where S_n is the sum of the first n terms, a₁ is the first term, and a_n is the nth term.

For our triangular number, we have:

T₂₀ = S₂₀ = 20/2 * (1 + 20) = 10 * 21 = 210

Conclusion

Therefore, the 20th triangular number is 210.

Answer

20th triangular number are