1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ozzi
3 years ago
7

Find d for the arithmetic series with S17=-170 and a1=2

Mathematics
1 answer:
Irina18 [472]3 years ago
6 0
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}

well, since the 17th term is that much, let's check what "d" is then anyway,

\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
n=17\\
a_{17}=-22\\
a_1=2
\end{cases}
\\\\\\
-22=2+(17-1)d\implies -22=2+16d\implies -24=16d
\\\\\\
\cfrac{-24}{16}=d\implies -\cfrac{3}{2}=d
You might be interested in
.<br>2. Two angles forming a linear pair are always​
dezoksy [38]

Answer:

Intersect

Step-by-step explanation:

A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees

5 0
2 years ago
I don’t know if this is right, I’m stuck. Help!
STALIN [3.7K]

Answer:

C

Step-by-step explanation:

According to SohCahToa, cosine is adjacent over the hypotenuse.

The adjacent when looking from angle b, is 21.

The hypotenuse of this triangle is 29.

So Cos B=21/29

5 0
3 years ago
Which function has the same domain as y=2.VX?
Musya8 [376]

Answer:

use an online calculator is the best option

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Jack says if you multiply a number by a fraction the product will always be smaller than what you started with. Is he correct? W
Alexus [3.1K]

Answer:

true and false

Step-by-step explanation:

6 0
3 years ago
PLS HELP HELP PLSZZZZZ
Dmitry_Shevchenko [17]

Answer:

cant see  the pic.

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Other questions:
  • Heather was asked to graph 3x - y = -4 by using slope and y-intercept. Her graph is shown.
    10·1 answer
  • The Baltimore Ravens scored 35 more than three times the number of points the Pittsburgh Steelers scored. Altogether, the teams
    14·1 answer
  • A chess set is on sale for $75.00, which is 40% off of its original price. What was the original price of the chess set?
    12·1 answer
  • Under root 12+ under root 12+ under root 12+ ......
    10·1 answer
  • A. X= 49/3<br> B. X= 21<br> C. X= 51<br> D. X= 9
    15·1 answer
  • In the figure below find the area of the shaded triangle XYZ. help me pliz
    10·2 answers
  • A new car valued at 24,000 depreciates at 9% per year. What is the value of the car one year after purchase?
    10·1 answer
  • Pls Answer This gyys ​
    15·2 answers
  • What is the approximate line of best fit for the scatter plot
    15·1 answer
  • Determine the standard form of the equation of the line that passes through (6, -9) and (-8, 6)
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!