Answer:
1)[tex]a_{n}=a_{1}+(n-1)d\Rightarrow a_{n}=-1-2(n-1)\\a_{2}=-1-2(2-1)\Rightarrow a_{2}=-3\\a_{3}=-1-2(3-1)\Rightarrow a_{3}=-5\\(...)\\a_{10}=-1-2(10-1)=-19[/tex]
2) [tex]a_{10}=4+8(10-1)\Rightarrow a_{10}=76[/tex]
Step-by-step explanation:
1) To write an Arithmetic Sequence, as an Explicit Term, is to write a general formula to find any term for this sequence following this pattern:
[tex]a_{n}=a_{1}+d(n-1)\Rightarrow \left\{\begin{matrix}a_{n}=n^{th}\: term\\a_1=1st \: term \\d=\: difference\\n=n^{th}\, term\end{matrix}\right.[/tex]
"Write an explicit formula for each explicit formula A(n)=-1+(n-1)(-2)"
This isn't quite clear. So, assuming you meant
Write an explicit formula for each term of this sequence A(n)=-1+(n-1)(-2)
As this A(n)=-1+(n-1)(-2) Â is already an Explicit Formula, since it is given the first term [tex]a_{1}=-1[/tex] the common difference [tex]d=-2[/tex] let's find some terms of this Sequence through this Explicit Formula:
[tex]a_{n}=a_{1}+(n-1)d\Rightarrow a_{n}=-1-2(n-1)\\a_{2}=-1-2(2-1)\Rightarrow a_{2}=-3\\a_{3}=-1-2(3-1)\Rightarrow a_{3}=-5\\(...)\\a_{10}=-1-2(10-1)=-19[/tex]
2) [tex](4,12,20,28, ..)[/tex] In this Arithmetic Sequence the common difference is 8, the first term value is 4.
Then, just plug in the first term and the common difference into the explicit formula:
[tex]a_{10}=4+8(10-1)\Rightarrow a_{10}=76[/tex]
