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.
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.