SOLUTION: 2, 4 , 6, 8 , Explicit formula? 2, 6, 18, 54, Explicit formula? 3, 6, 12, 24, Explicit formula? 2, 3, 4.5, 6.75 Explicit formula?

Algebra ->  Formulas -> SOLUTION: 2, 4 , 6, 8 , Explicit formula? 2, 6, 18, 54, Explicit formula? 3, 6, 12, 24, Explicit formula? 2, 3, 4.5, 6.75 Explicit formula?       Log On


   



Question 1194958: 2, 4 , 6, 8 , Explicit formula?
2, 6, 18, 54, Explicit formula?
3, 6, 12, 24, Explicit formula?
2, 3, 4.5, 6.75 Explicit formula?

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1. 2, 4+, 6, 8 ,
here we need the formula for nth term of an arithmetic progression is
a%5Bn%5D=a%5B1%5D%2Bd%28n-1%29
note that the difference between terms is 2
In this example we have a%5B1%5D=2 and d=2
a%5Bn%5D=2%2B2%28n-1%29
a%5Bn%5D=2%2B2n-2
a%5Bn%5D=2n where n=1,2,3,...


2. 2, 6, 18, 54,

here we need the formula for nth term of a geometric progression which is
a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29
a%5B1%5D=2
r=6%2F2=3
a%5Bn%5D=2%2A3%5E%28n-1%29 where n=1,2,3,...


3. 3,+6, 12, 24,
this is also a geometric progression
a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29
a%5B1%5D=3%7D%5D%5D%0D%0A%5B%7B%7Br=6%2F3=2
a%5Bn%5D=3%2A2%5E%28n-1%29 where n=1,2,3,...

4.
2, 3,+4.5, 6.75
rewrite sequence as 2, 3, 9%2F2, 27%2F4
this is also a geometric progression
a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29
a%5B1%5D=2
r=%2827%2F4%29%2F%289%2F2%29=3%2F2
a%5Bn%5D=2%2A%283%2F2%29%5E%28n-1%29+where n=1,2,3,...