Question

What is the sequence of 1,-2,3,-4,5

Answer 1

Notice that the sequence of the absolute values of the given sequence is just the sequence of the natural numbers:

`1,2,3,4,5,\ldots`

Nevertheless, the sign of each member of the sequence alternates between positive and negative:

`+,-,+,-,+,\ldots`

We can explicitly represent the n-th term of the sequence as:

`a_n=n*(-1)^(n-1)`

Verify this expression for the first 3 terms:

`\begin{gathered} a_1=1*(-1)^(1-1)=1*(-1)^0=1*1=1 \\ a_2=2*(-1)^(2-1)=2*(-1)^1=2*(-1)=-2 \\ a_3=3*(-1)^(3-1)=3*(-1)^2=3*1=3 \\ \ldots \end{gathered}`

Therefore, an explicit formula for the n-th term of the given sequence, is:

`a_n=n*(-1)^(n-1)`