Consider the recurrence relation a_n = a_{n-1} + $n$ with initial condition a_1 = 1. The value of a_{13} is ________.

Step 1 (Expand the recurrence relation): We are given the recurrence relation $a_n=a_{n-1}+n$ with initial condition $a_1=1$. Let's write out consecutive terms:

• $a_2=a_1+2=1+2$

• $a_3=a_2+3=1+2+3$

• $a_n=1+2+3+\cdots +n$

Step 2 (Apply Arithmetic Sum Formula): The sum of the first $n$ natural numbers is:

Step 3 (Calculate a_13): Substituting $n=13$:

Step 4 (Conclusion): The value of $a_{13}$ is exactly 91.