What is the relation between each term and its position in the sequence?
Pattern: 2(1)-110(1), 2(2)-110(2), 2(3)-110(3), 2(4)-110(4) Next Term: a_5= 950 Rule for the nth Term: a_n= 2n-110n
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
1/10 &→& 3/20 &→& 5/30 &→& 7/40
Each term a_n can be written as two times its position n minus one, divided by ten multiplied by n.
Term
Pattern
Result
a_1
2( 1) - 1/10( 1)
1/10
a_2
2( 2) - 1/10( 2)
3/20
a_3
2( 3) - 1/10( 3)
5/30
a_4
2( 4) - 1/10( 4)
7/40
We can write the next term a_5 by following this pattern.
a_5=2( 5) - 1/10( 5)=9/50
Finally, considering the pattern of the sequence, we can write its rule.
a_n= 2 n -1 10 n
