+73 What are the first 4 terms of a sequence with an explicit formula an = 6 • (2)n-1 ?
+2446 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.
