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:
8 cups is greater then 8 oz
Step-by-step explanation:
Answer:
x=−2 or x=4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
x2−2x−3=5
Step 2: Subtract 5 from both sides.
x2−2x−3−5=5−5
x2−2x−8=0
Step 3: Factor left side of equation.
(x+2)(x−4)=0
Step 4: Set factors equal to 0.
x+2=0 or x−4=0
x=−2 or x=4
Answer:
3.762 x 10^-7
Step-by-step explanation:
Alright this has the same exact concept as other scientific notation problems.
First, multiply your first numbers: 4.18 x 9 = 37.62
Next, we add our powers together -4 +-4 = -8 (can also be read as -4 - 4 = -8)
We now have 37.62 x 10^-8
Wait! This isn't in scientific notation.
Taking a closer look at this we see 37.62 x 10^-8 can be adjusted by moving the decimal over to the left. Scientific notation must be in simplest form with only one number on the left of the decimal. This gives up 3.762.
Now we need to adjust our notation. Since we moved the decimal over one we are adding one more power to our problem.
Our current power of -8 is now adding a power due to moving the decimal place over one unit to the left. This is equivalent to saying -8 + 1 which equals -7. Now that we fixed our powers, we can put our equation back together for our final answer
3.762 x 10^-7