The given formula means that, after the first term of the sequence, every term a_(n+1) is the difference of 2 times the previous term a_n and 5.
5, 5, 5, 5, 5
Practice makes perfect
We are asked to write the first five terms of a sequence, given a recursive formula.
a_1&=5
a_(n+1)&=2a_n-5
To do so, we will use a table. Notice that to find a_2 we will substitute n=1, to find a_3 we will substitute n=2, and so on.
n
a_(n+1)=2a_n-5
2a_n-5
a_(n+1)
-
a_1=5
-
5
1
a_(1+1)=2a_1-5
2 a_1-5=2( 5)-5
5
2
a_(2+1)=2a_2-5
2 a_2-5=2( 5)-5
5
3
a_(3+1)=2a_3-5
2 a_3-5=2( 5)-5
5
4
a_(4+1)=2a_4-5
2 a_4-5=2( 5)-5
5
Therefore, the first five terms of the sequence are 5, 5, 5, 5, and 5.
