Question

What is the recursive formula using 23 and 114, when 23 is the first term and 114 is the second?

Answer 1

The series is an arithmetic series so it is given that:

`\begin{gathered} a_1=23,a_2=114 \\ d=a_2-a_1 \\ d=114-23=91 \end{gathered}`

The nth term of the series is given by:

`\begin{gathered} a_n=a_1+(n-1)(d) \\ a_n=23+(n-1)91 \\ a_n=23+91n-91 \\ a_n=91n-68\ldots(i) \end{gathered}`

The (n-1)th term is given by:

`\begin{gathered} a_(n-1)=91(n-1)-68 \\ a_(n-1)=91n-91-68 \\ a_(n-1)=91n-159\ldots(ii) \end{gathered}`

Subtract (ii) from (i) to get:

`\begin{gathered} a_n-a_(n-1)=-68-(-159) \\ a_n-a_(n-1)=91 \\ a_n=a_(n-1)+91\ldots(iii) \end{gathered}`

So the recursive formula is given by equation (iii) shown above.