Question

For the following sequence, state the common difference, identify which is the explicit form and which is the recursive form of the rule, and find the term listed.Sequence: 0,100,200,300,…Common difference: ?An=-100+100nexplicit or recursive?An=an-1+100A1=0Explicit or recursive?

Answer 1

Give the sequence:

`0,\text{ 100, 200, 300,..}`

The common difference is the difference between two consecutive terms.

Thus, the common diffrence is evaluated as

`\begin{gathered} 100-0 \\ =100 \end{gathered}`

Thus, from the explicit formula,

`\begin{gathered} a_n=a+(n-1)d \\ where \\ a=0 \\ d=100 \end{gathered}`

The explicit form is evaluated to be

`\begin{gathered} a_n=0+(n-1)100 \\ \implies\text{A}_n=-100+100n \end{gathered}`

The recursive form is evaluated as