Question 1185339
A) Find the sum of the first 8 terms
<pre>
{{{S[infinity]}}}{{{""=""}}}{{{a[1]/(1-r^"")}}}

{{{200}}}{{{""=""}}}{{{4^""/(1-r^"")}}}

{{{200(1-r)}}}{{{""=""}}}{{{4}}}

Divide both sides by 4

{{{50(1-r)}}}{{{""=""}}}{{{1}}}

{{{50-50r}}}{{{""=""}}}{{{1}}}

{{{-50r}}}{{{""=""}}}{{{-49}}}

{{{r}}}{{{""=""}}}{{{49/50}}}

{{{r}}}{{{""=""}}}{{{0.98}}}

{{{S[n]}}}{{{""=""}}}{{{a[1](1-r^n)/(1-r^"")}}}

{{{S[8]}}}{{{""=""}}}{{{4(1-0.98^8)/(1-0.98^"")}}}

{{{S[8]}}}{{{""=""}}}{{{29.84739548}}}</pre>

b) Find the least value for n which Sn > 163.<pre>

{{{S[n]}}}{{{""=""}}}{{{4(1-0.98^n)/(1-0.98^"")}}}{{{"">""}}}{{{163}}}

{{{(4/.02)(1-0.98^n)}}}{{{"">""}}}{{{163}}}

{{{200(1-0.98^n)}}}{{{"">""}}}{{{163}}}

{{{1-0.98^n}}}{{{"">""}}}{{{163/200}}}

{{{1-0.98^n}}}{{{"">""}}}{{{0.815}}}

{{{-0.98^n}}}{{{"">""}}}{{{-0.185}}}

{{{0.98^n}}}{{{"">""}}}{{{0.185}}}

Take natural logs of both side:

{{{ln(0.98^n)}}}{{{"">""}}}{{{ln(0.185)}}}

{{{n*ln(0.98)}}}{{{"">""}}}{{{ln(0.185)}}}

{{{n}}}{{{"">""}}}{{{ln(0.185)/ln(0.98)}}}

{{{n}}}{{{"">""}}}{{{83.52343215}}}

The least integer than n can take on greater 
than that is 84.

Edwin</pre>