Question

Write a recursive definition for the sequence below.

-1, 4, 9, 14, ...

Answer 1

Answer: $a_{1}$=-1 ; $a_{n}$=$a_{n-1}$ +5

Step-by-step explanation: clearly,  $a_{1}$=-1

now,  $a_{2}$= $a_{1}$+5

                                    =-1+5

                                    =4

$a_{3}$= $a_{2}$+5

                          =4+5

                          =9

So, in general,  $a_{n}$=$a_{n-1}$ +5

Answer 2

By identifying type of sequence  we got that recursive definition for the sequence -1,4,9,14... is  $a_n=a_{n-1}+5$

What is a sequence ?

A sequence is collection of numbers with a particular pattern.

Here given sequence is

-1,4,9,14...

$a_1=-1\\\\a_2=4\\\\a_3=9\\\\a_4=14\\\\\\a_2-a_1=4+1=5\\\\a_3-a_2=9-4=5\\\\a_4-a_3=14-9=5$

Hence this is an AP with a=-1 and d=5

So general term of this  AP can be written as

So difference of any consecutive terms is equal to 5

$a_n-a_{n-1}=5\\\\a_n=a_{n-1}+5$

By identifying type of sequence we got that recursive definition for the sequence -1,4,9,14... is  $a_n=a_{n-1}+5$

To learn more about sequence visit : brainly.com/question/6561461