What is the relation between any two consecutive terms?
Pattern: Arithmetic Next Term: a_6=- 2.2 Rule for the nth Term: a_n=- 1.6n+7.4
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 && a_5
5.8 &→& 4.2 &→& 2.6 &→& 1 &→& - 0.6
We can see that the difference between any two consecutive terms is always - 1.6. Therefore, we have an arithmetic sequence with a common difference of - 1.6. To find the 6th term, we will add - 1.6 to the 5th term.
a_6=- 0.6+( - 1.6)= - 2.2
Finally, considering that we have an arithmetic sequence with a first term of 5.8 and a common difference of - 1.6, we can write its rule.
a_n= a_1+(n-1) d
⇓
a_n= 5.8+(n-1)( - 1.6)
a_n=- 1.6n+7.4
