So, we know the sum of the first 17 terms is -170, thus S₁₇ = -170, and we also know the first term is 2, well
![\bf \textit{ sum of a finite arithmetic sequence}\\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ ----------\\ n=17\\ S_{17}=-170\\ a_1=2 \end{cases} \\\\\\ -170=\cfrac{17(2+a_{17})}{2}\implies \cfrac{-170}{17}=\cfrac{(2+a_{17})}{2} \\\\\\ -10=\cfrac{(2+a_{17})}{2}\implies -20=2+a_{17}\implies -22=a_{17}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7B%20sum%20of%20a%20finite%20arithmetic%20sequence%7D%5C%5C%5C%5C%0AS_n%3D%5Ccfrac%7Bn%28a_1%2Ba_n%29%7D%7B2%7D%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0An%3Dn%5E%7Bth%7D%5C%20term%5C%5C%0Aa_1%3D%5Ctextit%7Bfirst%20term%27s%20value%7D%5C%5C%0A----------%5C%5C%0An%3D17%5C%5C%0AS_%7B17%7D%3D-170%5C%5C%0Aa_1%3D2%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A-170%3D%5Ccfrac%7B17%282%2Ba_%7B17%7D%29%7D%7B2%7D%5Cimplies%20%5Ccfrac%7B-170%7D%7B17%7D%3D%5Ccfrac%7B%282%2Ba_%7B17%7D%29%7D%7B2%7D%0A%5C%5C%5C%5C%5C%5C%0A-10%3D%5Ccfrac%7B%282%2Ba_%7B17%7D%29%7D%7B2%7D%5Cimplies%20-20%3D2%2Ba_%7B17%7D%5Cimplies%20-22%3Da_%7B17%7D)
well, since the 17th term is that much, let's check what "d" is then anyway,
Answer:
Equation: y =
x
21/2 cups of water
Step-by-step explanation:
Plug in 7 as y and 4 as x
7 = 4k
Find k
k = 7/4
Then plug k into th equation
y = 7/4 x
For the second part of the question:
Plug in x which is 6 into the bolded equation.
y = (7/4)(6) = 42/4 = 21/2 (simplified form)
21/2 cups of water
Answer:
No
Step-by-step explanation: