Question 1168724: Find the formula an for the following sequences:
1. 3, 4, 5, 6, 7,…
2. 2, 5, 10, 17, 26,…
3. √3, 3, 3√3, 9,…
4. 4/1, 9/2, 16/3, 25/4,…
5. - ½, 1/3, -1/4,…
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! this is of the form 3+(n-1)1 or more simply, (n+2). The differences are the same 1/1/1/1 so it is first power.
-
this has differences of 3/5/7/9
and they have differences of 2/2/2
this makes it a quadratic
n=1, value is 2
so a(1)^2+b+c=2; a+b+c=2
and 4a+2b+c=5
and 9a+3b+c=10
subtract second from third; first from second
5a+b=5
3a+b=3
subtract second from first
2a=2
a=1, b=0
so n^2 is first term and b=0, c=1
(n^2+1) is the formula for an
a4=17 a5=26 etc.
-
This has a ratio of sqrt(3)
a1=sqrt(3)^n=sqrt(3)
a2=sqrt(3)^2=3, etc.
-
This has a ratio of 2^2/1; 3^2/2; 4^3/3, 5^2/4
(n1+1)^2/n1
-
this has a -(1)/(n+1) form and the minus sign is first, matching the odd number.
an=-1^(n)/(n+1); -1/2, 1/3, -1/4
|
|
|
