Question 474095
A Daily Tripling Salary:
Suppose someone offered you a job for 10 days under the following conditions. You will be paid $5 for the first day, $15 for the second, and $45 for the third, and so on, tripling your previous day's salary each day. How much would you earn altogether?
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The salary represents a geometric sequence with common ratio 3.
The sum of the 1st n terms of a geometric sequence is
{{{S_n = a1(1-r^n)/(1-r)}}} where r = the common ratio, a1 = the 1st term
So the total salary after the 10th day would be:
{{{S_10 = 5(1-3^10)/(1-3)}}}
This gives S_10 = $147,620