What is the relation between any two consecutive terms?
Pattern: Arithmetic Next Term: a_5=21 Rule for the nth Term: a_n=5n-4
Practice makes perfect
Let's start by paying close attention to the terms of the given sequence.
cccc
a_1 && a_2 && a_3 && a_4
1 &→& 6 &→& 11 &→& 16
We can see that the difference between any two consecutive terms is always 5. Therefore, we have an arithmetic sequence with a common difference of 5. To find the 5th term, we will add 5 to the 4th term.
a_5=16+ 5=21
Finally, considering that we have an arithmetic sequence with a first term of 1 and a common difference of 5, we can write its rule.
a_n= a_1+(n-1) d
⇓
a_n= 1+(n-1) 5
a_n=5n-4
