Answer:
The sequence of numbers 1, 3, 6, 10 corresponds to the triangular numbers. Triangular numbers are those that can be arranged in an equilateral triangle. They are given by the formula:
\[ T_n = \frac{n \cdot (n + 1)}{2} \]
where \( T_n \) represents the \( n \)-th triangular number.
Let's find the 10th triangular number using the formula:
\[ T_{10} = \frac{10 \cdot (10 + 1)}{2} \]
\[ T_{10} = \frac{10 \cdot 11}{2} \]
\[ T_{10} = \frac{110}{2} \]
\[ T_{10} = 55 \]
Therefore, the 10th triangular number is \( \boxed{55} \).
Answer: MARK AS BRAINLIST
Step-by-step explanation:
The sequence of numbers 1, 3, 6, 10, ... follows a specific pattern where each subsequent number is obtained by adding the next natural number to the previous number. This sequence represents the triangular numbers.
To find the 10th number in this sequence, we can use the formula for the nth triangular number:
\[ T_n = \frac{n(n+1)}{2} \]
Let's apply this formula to find the 10th triangular number:
\[ T_{10} = \frac{10 \cdot (10 + 1)}{2} \]
\[ T_{10} = \frac{10 \cdot 11}{2} \]
\[ T_{10} = \frac{110}{2} \]
\[ T_{10} = 55 \]
Therefore, the 10th number in the sequence 1, 3, 6, 10, ... is \( \boxed{55} \).
