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

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

Jun 2, 2018

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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.

Jun 2, 2018
edited by TheXSquaredFactor  Jun 2, 2018
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Thanks this helped!

GAMEMASTERX40  Jun 2, 2018