What is the relation between each term and its position in the sequence?
Pattern: 4* 1(- 1)^1, 4* 2(- 1)^2, 4* 3(- 1)^3, 4* 4(- 1)^4
Next Term: a_5=- 20 Rule for the nth Term: a_n=4 n(- 1)^n
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
- 4 &→& 8 &→& - 12 &→& 16
Each term a_n can be written as four multiplied by its position n, times negative one to the power of n.
Term
Pattern
Result
a_1
4* 1( - 1)^1
- 4
a_2
4* 2( - 1)^2
8
a_3
4* 3( - 1)^3
- 12
a_4
4* 4( - 1)^4
- 16
We can write the next term a_5 by following this pattern.
a_5= 4* 5( - 1)^5=- 20
Finally, considering the pattern of the sequence, we can write its rule.
a_n= 4 n( - 1)^n
