1

So if I borrow money and, to pay it back, I pay 50 for my first month and then 25 more each additional month for 12 months, How much am I paying in total after 12 months?

I’m thinking $a_1=50$ and $d=25$ so $a_{12}=(n-1) \cdot 25+50$ right? So $a_{12}=325$?

Secondly if an object is falling and it falls $16$ feet in the first second, $48$ in the next second, and $80$ feet for the third second, then how many feel will the object fall in 10 seconds?

So $a_{10}=(n-1) \cdot 32+16$ or $a_{10}=304$ feet.

Are my set ups correct? I can add in more if my work but I’m honestly most concerned that I’m setting my series formula correctly.

Vasili
  • 10,690
K Math
  • 1,245
  • 1
  • 11
  • 21

1 Answers1

1

For the first part, we do have $a_{12}=325$ but it seems to me that the question is asking about how much one has paid in total. So perhaps the relevant formula is

$$S_{n}=\frac{n}2(2a+(n-1)d)$$

For the second question, it seems to be asking for how many feet the object will fall in $10$ seconds rather than the falling distance in $10^{th}$ second.

Siong Thye Goh
  • 149,520
  • 20
  • 88
  • 149
  • The formula you gave me is the same one I’m using. Also for 2, isn’t finding the distance at the 10th second the same as how far it will fall in 10 seconds? – K Math Oct 18 '18 at 11:15
  • I am not sure if they are asking from time $0$ to time $10$ second, how far has it fallen? or are they asking in the $10$th second. but it is more of an english problem. It's like how tall will a child grow in $10$ years vs how tall will a child grow in the tenth year to me. – Siong Thye Goh Oct 18 '18 at 11:36