Question

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

a1=10 and an-1+3 for n is greater than and equal to 2

Answer 1

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

Step-by-step 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.