What is the relation between any two consecutive terms?
Pattern: Arithmetic Next Term: a_5= 54 Rule for the nth Term: a_n= n4
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
1/4 &→& 2/4 &→& 3/4 &→& 4/4
We can see that the difference between any two consecutive terms is always 14. Therefore, we have an arithmetic sequence with a common difference of 14. To find the 5th term, we will add 14 to the 4th term.
a_5=4/4+ 1/4=5/4
Finally, considering that we have an arithmetic sequence with a first term of 14 and a common difference of 14, we can write its rule.
a_n= a_1+(n-1) d
⇓
a_n= 1/4+(n-1) 1/4 [0.5em]
a_n=n/4
