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What are the first 4 terms of a sequence with an explicit formula a= 6 • (2)n-1 ?

GAMEMASTERX40  Jun 2, 2018
 #1
avatar+2294 
+2

Hi, Rick, I will find the first two terms, and I want to see you find the next two. See if you can do it!

 

There are a few aspects of the given explicit formula.

 

n = the term number

an = the value of the nth term.

 

The problem asks for the first 4 terms. I will start with the first term. Since n represents the term number and since we want the first term, n=1:

 

\(n=1;\\ a_n=6\cdot(2)^{n-1}\)Replace all instances of n with a 1 and solve for the first term!
\(a_1=6\cdot(2)^{1-1}\)We can now simplify the exponent. 
\(\)\(a_1=6\cdot2^0\)Via the exponent properties,  \(x^0=1, x\neq 0\).
\(a_1=6\)a1 , the value of the 1st term, is 6. That's what the notation means.
  

 

In order to find the 2nd term, set n to 2 and solve for a2:

 

\(n=2;\\ a_n=6\cdot(2)^{n-1}\)The process is no different than what occurred above. The only difference is the value of n.
\(a_2=6\cdot(2)^{2-1}\)Simplify the expression in the exponent.
\(a_2=6\cdot 2^1\) 
\(a_2=12\) 
  

 

Now, I am leaving the rest up to you. See what you can do.

TheXSquaredFactor  Jun 2, 2018
edited by TheXSquaredFactor  Jun 2, 2018
 #2
avatar+991 
+2

Thanks this helped!

GAMEMASTERX40  Jun 2, 2018

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