Save That Money!

Algebra Level pending

Hsu decides to save some money to buy a new phone. He does not know how much the phone is, so he wants to save money throughout January. He will save 1 cent on January 1 s t 1^{st} , 4 cents for the 2 n d 2^{nd} day, 10 cents on the 3 r d 3^{rd} day, 19 cents on the following day, 31 cents on the 5 t h 5^{th} day, and so on for the month. How much money will Hsu have saved in January?

Express your answer in dollars and cents (Ex. $178.82 would be inputted as 178.82)

NOTES :

  • January has 31 days

  • He does not save any other money not stated in the problem

  • Don't bash it!


The answer is 149.11.

Andrew The by Andrew The , 25, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Rama Devi
Jun 3, 2015

The sequence is nothing but the sequence of centered triangular numbers .Therefore the sum of first centered triangular numbers is the answer.Therefore the answer is 149.11.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Arjen Vreugdenhil
Sep 29, 2015

∑ n = 1 31 [ 1 + 3 ( n 2 ) ] = 31 + 3 ( 32 3 ) = 31 + 3 ⋅ 32 ⋅ 31 ⋅ 30 3 ⋅ 2 ⋅ 1 = 14911 cents . \sum_{n = 1}^{31} \left[1 + 3\left(\begin{array}{c} n \\ 2\end{array}\right)\right] = 31 + 3\left(\begin{array}{c} 32 \\ 3\end{array}\right) = 31 + 3\cdot\frac{32\cdot 31\cdot 30}{3\cdot 2 \cdot 1} = 14911\ \text{cents}.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...