Question

What is the recursive formula using 23 and 114? Here 23 is the first term and 114 is the common difference.

Answer 1

It is given that the first term is 23 and the differnce is 114 so it follows:

$a=23,d=114$

The nth term of the series is given by:

$\begin{gathered} a_n=a+(n-1)d \\ a_n=23+(n-1)(114) \\ a_n=23+114n-114 \\ a_n=114n-91\ldots(i) \end{gathered}$

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

$\begin{gathered} a_{n-1}=114(n-1)-91 \\ a_{n-1}=114n-114-91 \\ a_{n-1}=114n-205\ldots(ii) \end{gathered}$

Subtract (ii) from (i) to get:

$\begin{gathered} a_n-a_{n-1}=-91-(-205) \\ a_n=a_{n-1}+114\ldots(iii) \end{gathered}$

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