Question

The sequence shown below is defined using a recursion formula. Write the first four terms of the sequence.

Answer 1

Answer:

Step-by-step explanation:

a1=10

a_{n}=a_{n-1}+3

n=2

$a_{2}=a_{1}+3=10+3=13\\n=3\\a_{3}=a_{2}+3=13+3=16\\n=4\\a_{4}=a_{3}+3=16+3=19\\first~four~terms~are\\10,13,16,19$

Answer 2

Answer:  10, 13, 16, 19

Explanation:

The notation $a_1 = 10$ says that the first term is 10.

The notation $a_n = a_{n-1}+3$ is the recursive rule that says "to find the nth term, we add 3 to the previous term". So we add 3 to each term to get the next one.

• first = 10
• second = first+3 = 10+3 = 13
• third = second+3 = 13+3 = 16
• fourth = third + 3 = 16+3 = 19

This sequence is arithmetic due to the common difference d = 3.