Question

Please help me with these two math problems that I do not quite understand. This is urgent!

Write an explicit formula for each explicit formula A(n)=-1+(n-1)(-2)

Describe and correct the error at the right in finding the tenth term of the arithmetic sequence 4,12,20,28.

Answer 1

1)
`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`

2)
`a_(10)=4+8(10-1)\Rightarrow a_(10)=76`

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:

`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.`

"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) is already an Explicit Formula, since it is given the first term
`a_(1)=-1` the common difference
`d=-2` let's find some terms of this Sequence through this Explicit Formula:

`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`

2)
`(4,12,20,28, ..)` 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:

`a_(10)=4+8(10-1)\Rightarrow a_(10)=76`