• Nov 7th 2008, 09:58 PM
juliak
In a question:
Find the general term of Un which has U3 = 16 and U8=512

--> I got the answer of Un=4*2^n-1
which is correct,
however,
Un=4*2^n-1(=2^n+1)

What does (=2^n+1) mean and where did they get it from?

Thank you :D
• Nov 7th 2008, 10:13 PM
mr fantastic
Quote:

Originally Posted by juliak
In a question:
Find the general term of Un which has U3 = 16 and U8=512

--> I got the answer of Un=4*2^n-1
which is correct,
however,
Un=4*2^n-1(=2^n+1)

What does (=2^n+1) mean and where did they get it from?

Thank you :D

$\displaystyle 4 \times 2^{n-1} = 2^2 \times 2^{n-1}$. Do I need to spell it out from here ....?
• Nov 8th 2008, 03:42 AM
Soroban
Hello, juliak!

Your work is correct . . . but it can be simplified.

Quote:

Find the general term of $\displaystyle U_n$ where: $\displaystyle U_3 = 16\text{ and }U_8=512$

I got the answer of: .$\displaystyle U_n\:=\:4\cdot2^{n-1}$

however, the answer was this: .$\displaystyle U_n \:=\:2^{n+1}$

We have: .$\displaystyle U_n \:=\:4\cdot2^{n-1} \;=\;2^2\cdot2^{n-1} \;=\;2^{n+1}$

Got it?