What is the relation between each term and its position in the sequence?
Pattern: 23(1), 23(2), 23(3), 23(4) Next Term: a_5= 215 Rule for the nth Term: a_n= 23n
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
2/3 &→& 2/6 &→& 2/9 &→& 2/12
Each term a_n can be written as two over three times its position n.
Term
Pattern
Result
a_1
2/3( 1)
2/3
a_2
2/3( 2)
2/6
a_3
2/3( 3)
2/9
a_4
2/3( 4)
2/12
We can write the next term a_5 by following this pattern.
a_5=2/3( 5)=2/15
Finally, considering the pattern of the sequence, we can write its rule.
a_n=2/3 n
