Final answer:
To determine the value of a_{3} in the recursive sequence with a_{1} = 10 and a_{n} = a_{n-1} + 3, we calculate a_{2} as 13 and subsequently a_{3} as 16.
Step-by-step explanation:
How to Find the Value of a_{3}
Given the recursive formula for a sequence where a_{1} = 10 and a_{n} is defined by a_{n} = a_{n-1} + 3, we are tasked with finding the value of a_{3}.
To begin, we need to find the value of a_{2} before we can find a_{3} since this is a recursive sequence. Starting with a_{1}, we apply the given formula:
a_{2} = a_{1} + 3 = 10 + 3 = 13
a_{3} = a_{2} + 3 = 13 + 3 = 16
Therefore, the value of a_{3} is 16.