What is the relation between each term and its position in the sequence?
Pattern: 1^2+0.2, 2^2+0.2, 3^2+0.2, 4^2+0.2 Next Term: a_5=25.2 Rule for the nth Term: a_n=n^2+0.2
Practice makes perfect
Let's start by paying close attention to the terms of the given sequence.
ccccccc
a_1 && a_2 && a_3 && a_4
1.2 &→& 4.2 &→& 9.2 &→& 16.2
Each term a_n can be written as its position n squared plus point two.
Term
Pattern
Result
a_1
1^2 + 0.2
1.2
a_2
2^2 + 0.2
4.2
a_3
3^2 + 0.2
9.2
a_4
4^2 + 0.2
16.2
We can write the next term a_5 by following this pattern.
a_5= 5^2 + 0.2=25.2
Finally, considering the pattern of the sequence, we can write its rule.
a_n= n^2 + 0.2
