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

User Gaganshera
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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.

User Slvn
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