Answer:
Option 1 is correct.
Recursive formula - [tex]a_n=a_{n-1}+13[/tex] where [tex]a_1=5[/tex]
The next term is 70
Step-by-step explanation:
Given : The sequence 5, 18, 31, 44, 57, …
To find : The recursive formula and then find the next term.
Solution :
First we determine the terms
First term [tex]a_1=5[/tex]
We see that the common difference in the sequence is 18-5=31-18..=13
So, d=13
The recursive formula of the sequence is
[tex]a_n=a_{n-1}+13[/tex] where [tex]a_1=5[/tex]
satisfying the sequence 5, 18, 31, 44, 57, …
Now, to find 6th term of the sequence put n=6
[tex]a_n=a_{n-1}+13[/tex]
[tex]a_6=a_{6-1}+13[/tex]
[tex]a_6=a_{5}+13[/tex]
[tex]a_6=57+13[/tex]
[tex]a_6=70[/tex]
Therefore, Option 1 is correct. The next term is 70.
