Eli owes $605. The first week he will pay back $20. The second week he will pay back $29. The third week he will pay back $38. If Eli continues to pay the money back using the same sequence, how many weeks will it take him to pay back the entire amount?

Question

tkhunny · Answer

20 + (20+9) + (20+2*9) + (20+3*9) + ... + (20+(n-1)*9) >= 605

To be a little more clear:

(20+0*9) + (20+1*9) + (20+2*9) + (20+3*9) + ... + (20+(n-1)*9) >= 605

Now some algebra

20*n + 9*(0 + 1 + 2 + ... + (n-1)) >= 605

Or, rather than creating your own formula for the sum of an aritmetic series, you can use the formula for the sum given the first term of 20 and the common difference of 9.  :-)