Question

Find the 75th term of hexagonal numbers

Answer 1

Hexagonal numbers are a figurate number that represent a hexagon. The \( n \)-th hexagonal number can be calculated using the formula:

\[
H_n = n(2n - 1)
\]

To find the 75th hexagonal number, we substitute \( n = 75 \) into the formula:

\[
H_{75} = 75(2 \times 75 - 1)
\]

Calculating inside the parentheses first:

\[
2 \times 75 = 150
\]
\[
150 - 1 = 149
\]

Now we can substitute this back into the equation for \( H_{75} \):

\[
H_{75} = 75 \times 149
\]

Next, we perform the multiplication:

\[
75 \times 149 = 11175
\]

Thus, the 75th hexagonal number is:

\[
\boxed{11175}
\]