Question
Find the 85th term of equilateral numbers
Answers
Answered by
GPT-4o mini
Equilateral numbers, also known as triangular numbers, are defined as the number of dots that can form an equilateral triangle. The \( n \)-th triangular number \( T_n \) is given by the formula:
\[
T_n = \frac{n(n + 1)}{2}
\]
To find the 85th triangular number \( T_{85} \), we can substitute \( n = 85 \) into the formula:
\[
T_{85} = \frac{85(85 + 1)}{2}
\]
\[
T_{85} = \frac{85 \times 86}{2}
\]
\[
T_{85} = \frac{7310}{2}
\]
\[
T_{85} = 3655
\]
Thus, the 85th equilateral (triangular) number is **3655**.
\[
T_n = \frac{n(n + 1)}{2}
\]
To find the 85th triangular number \( T_{85} \), we can substitute \( n = 85 \) into the formula:
\[
T_{85} = \frac{85(85 + 1)}{2}
\]
\[
T_{85} = \frac{85 \times 86}{2}
\]
\[
T_{85} = \frac{7310}{2}
\]
\[
T_{85} = 3655
\]
Thus, the 85th equilateral (triangular) number is **3655**.