# expressions

• Feb 20th 2010, 05:21 PM
ashimashi
expressions
hi, i have a math problem

Term ......... . . Pattern
_________l__________________

...1 ............. 2
... 2 ............. 6
...3 ............. 18
...4 ............. 54
...5 ............. 162

so the pattern is start at 2 times 3 each time. but i need a expression

ex. n+5

N is the term, N and something else has to give me the pattern

• Feb 20th 2010, 05:31 PM
Prove It
Quote:

Originally Posted by ashimashi
hi, i have a math problem

Term ......... . . Pattern
_________l__________________

...1 ............. 2
... 2 ............. 6
...3 ............. 18
...4 ............. 54
...5 ............. 162

so the pattern is start at 2 times 3 each time. but i need a expression

ex. n+5

N is the term, N and something else has to give me the pattern

This is a geometric sequence, with $t_1 = 2, r = 3$.

In a geometric sequence $t_{n + 1} = rt_{n}$.

So $t_2 = 3\cdot 2$

$t_3 = 3\cdot 3 \cdot 2$

$t_4 = 3\cdot 3\cdot 3 \cdot 2$...

Can you see that $t_{n + 1} = 2\cdot 3^n$?
• Feb 20th 2010, 05:43 PM
ashimashi
kk thank you