Question 1188459
<pre>
The other solution is incorrect.

A well-known theorem states that the general (explicit) formula for the recursion formula 

{{{y[n]}}}{{{""=""}}}{{{A*y[n-1]+B}}} has the form {{{y[n]}}}{{{""=""}}}{{{C*A^n + D}}}

We calculate y(1) = 5.15, y(2) = 7.4075, substitute it and A=1.05

{{{5.15}}}{{{""=""}}}{{{C*1.05^1 + D}}}

{{{D}}}{{{""=""}}}{{{5.15-1.05C}}}

We calculate y(2) = 7.4075, substitute it and A=1.05

{{{7.4075}}}{{{""=""}}}{{{C*1.05^2 + D}}}

{{{7.4075}}}{{{""=""}}}{{{1.1025C + D}}}

{{{D}}}{{{""=""}}}{{{7.4075-1.1025C}}}

Equating the expressions for D

{{{5.15-1.05C}}}{{{""=""}}}{{{7.4075-1.1025C}}}

{{{0.0525C}}}{{{""=""}}}{{{2.2575}}}

{{{C}}}{{{""=""}}}{{{43}}}

{{{D}}}{{{""=""}}}{{{5.15-1.05(43)}}}

{{{D}}}{{{-40}}}

General (explicit) formula

{{{y[n]}}}{{{""=""}}}{{{43*1.05^N-40}}}

Edwin</pre>