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
Kitty [74]
4 years ago
5

PLEASE. NEED HELP. Find the sum.

Mathematics
1 answer:
VLD [36.1K]4 years ago
8 0

Distribute the sum:

\displaystyle\sum_{i=1}^{24}(3i-2)=3\sum_{i=1}^{24}i-2\sum_{i=1}^{24}1

Use the following formulas:

\displaystyle\sum_{i=1}^n1=n

\displaystyle\sum_{i=1}^ni=\dfrac{n(n+1)}2

\implies\displaystyle\sum_{i=1}^{24}(3i-2)=3\cdot\frac{24\cdot25}2-2\cdot24=\boxed{852}

In case you don't know where those formulas came from:

The first one is obvious; you're just adding <em>n</em> copies of 1, so 1 + 1 + ... + 1 = <em>n</em>.

The second can be proved in this way: let <em>S</em> be the sum 1 + 2 + 3 + ... + <em>n</em>. Rearrange it as <em>S</em> = <em>n</em> + (<em>n</em> - 1) + (<em>n</em> - 2) + ... + 1. Then 2<em>S</em> = (<em>n</em> + 1) + (<em>n</em> + 1) + (<em>n</em> + 1) + ... + (<em>n</em> + 1), or <em>n</em> copies of <em>n</em> + 1. So 2<em>S</em> = <em>n</em>(<em>n</em> + 1). Divide both sides by 2 and we're done.

You might be interested in
N exclusive club for top students has to elect a new president and treasurer. there are 50 students in the club, and all are eli
Novay_Z [31]
It sounds like the problem should read:
"An exclusive club for top students has to elect a new president and treasurer. There are 50 students in the club, and all are eligible for election. No person can have two jobs. How many different choices of officers are possible if:"

But then it trails off. It seems incomplete. Please update the problem with any missing information and/or instructions. Thank you.
8 0
4 years ago
Find the measure of
MatroZZZ [7]
Angles D and G are 80 degrees

8 0
3 years ago
If you figure out these questions I’ll give you brainliest
Naddika [18.5K]

Answer:

1: it is called a building cause it can still be improve or built on.

2: its an integer in a decimal formation.

3: cause each unit is apart from the other units even though it is 1 big building.

Step-by-step explanation:

7 0
3 years ago
Graph the line that has an x intercept (-3,0) and y intercept (0,-5)
Licemer1 [7]

Answer:

Step-by-step explanation:

Plot points at the given points and connect with a line.

6 0
4 years ago
PLEASE HELP!! 8th grade
schepotkina [342]
-1.5 !! this is easy hope this helps
4 0
3 years ago
Other questions:
  • Emily and Kayla collect seashells. Emily has 400 + 90 + 2 seashells. Kayla has four hundred ninety- four seashells. Emily and Ka
    9·1 answer
  • What is the solution to the system of linear equations?<br> (-3,0)<br> (-3, 3)<br> (0, 2)<br> (3, 1)
    13·1 answer
  • Which expression is even for all integers a and b?
    6·2 answers
  • ) You are finally well!  But now your child is sick!  You know there have been mistakes in orders so you are on the internet t
    8·1 answer
  • Can someone help me with question (b)??
    15·1 answer
  • Find x when y=5 in the literal equation 4x+7y=51
    7·1 answer
  • Find the value of c so that (x - 2) is a factor of the polynomial p(x).<br> p(x) = x5 - 4x3 + cx - 6
    14·1 answer
  • The set of points (4, 3), (7, 3), (4, 0), and (7, 0) identifies the vertices of a quadrilateral. Which is the most specific desc
    7·1 answer
  • Write the following expression in standard form by expanding and collecting like
    10·1 answer
  • Find the area of a circle with a radius of 21 inches. Use 22/7 for pi .
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!