What is the relation between any two consecutive terms?
Pattern: Arithmetic Next Term: a_5=40.2 Rule for the nth Term: a_n=7.8n+1.2
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
9 &→& 16.8 &→& 24.6 &→& 32.4
We can see that the difference between any two consecutive terms is always 7.8. Therefore, we have an arithmetic sequence with a common difference of 7.8. To find the 5th term, we will add 7.8 to the 4th term.
a_5=32.4+ 7.8=40.2
Finally, considering that we have an arithmetic sequence with a first term of 9 and a common difference of 7.8, we can write its rule.
a_n= a_1+(n-1) d
⇓
a_n= 9+(n-1) 7.8
a_n=7.8n+1.2
