What is the relation between each term and its position in the sequence?
Pattern: 2(1)2+1, 2(2)2+2, 2(3)2+3, 2(4)2+4
Next Term: a_5= 107 Rule for the nth Term: a_n= 2n2+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
2/3 &→& 4/4 &→& 6/5 &→& 8/6
Each term a_n can be written as two times its position n over two plus n.
Term
Pattern
Result
a_1
2( 1)/2 + 1
2/3
a_2
2( 2)/2 + 2
4/4
a_3
2( 3)/2 + 3
6/5
a_4
2( 4)/2 + 4
8/6
We can write the next term a_5 by following this pattern.
a_5=2( 5)/2 + 5=10/7
Finally, considering the pattern of the sequence, we can write its rule.
a_n=2 n/2 + n
