Question 1055333
If Sarah was saving for a computer that cost$1200 the first month she saved$20 and doubled the amount each month after that how many months will it take her to save the money?
<pre>Month 1: $20 saved
Month 2: 2(20), or $40 saved
Month 3: 2(40), or $80 saved

The above represents a GP with the following sequence: {{{a[n] = 20(2)^(n - 1)}}}, with:
n = number (month) of the sequence

We now use the sum of a GP, or {{{S[n] = (a[1] - a[n] * r)/(1 - r)}}}   
{{{"1,200" = (20 - a[n] * 2)/(1 - 2)}}} ------- Substituting {{{matrix(1,12, "1,200", for, S[n], ",", 20, for, a[1], ",", and, 2, for, r))}}}
{{{"1,200" = (20 - 2a[n])/(- 1))}}}
{{{20 - 2a[n] = - "1,200"}}} -------- Cross-multiplying
{{{- 2a[n] = - "1,200" - 20}}}
{{{- 2a[n] = - "1,220"}}}
{{{a[n] = "- 1,220"/(- 2)}}}, or $610

As seen above, the term, or month that she will have saved 1,200 or more is the one in which she has saved $610, or more

Now we see that: {{{a[n] = 20(2)^(n - 1)}}} becomes:
{{{610 = 20(2)^(n - 1)}}}
{{{610/20 = 2^(n - 1)}}} ------ Dividing by 20
{{{61/2 = 2^(n - 1)}}}
{{{log (2, (61/2)) = n - 1}}} ------- Converting to LOGARITHMIC form
n, or month in which she will have saved $610 = {{{log (2, (61/2)) + 1}}}, or {{{highlight_green(matrix(1,6, 5.930737, or, close, to, month, 6))}}}. 
This means that in month 5, she would NOT HAVE realized her goal of $1,200, but in month 6, she would’ve saved more than the $1,200 (see table below).


OR


<b><u>The EASIEST METHOD:</b></u>
Month     Amount Saved     Total Saved
  1           $20              $20
  2      2(20)  =  $40         $60
  3      2(40)  =  $80        $140
  4      2(80)  = $160        $300
  5      2(160) = $320        $620
  6      2(320) = $640      $1,260</pre>