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
Y_Kistochka [10]
3 years ago
9

Sum of 1+3+5+7+...+997

Mathematics
1 answer:
PilotLPTM [1.2K]3 years ago
4 0
1 + 3 + 5 + 7 + ... + 997

1, 3, 7, ... , 997 are terms of an arithmetic sequence

a_1=1;\ a_2=3;\ ...;\ a_n=997\\\\d=a_2-a_1\to d=3-1=2\\\\a_n=a_1+(n-1)d\\\\subtitute\\\\997=1+(n-1)\cdot2\\977=1+2n-2\\977=2n-1\ \ \ \ |add\ 1\ to\ both\ sides\\2n=998\ \ \ \ |divide\ both\ sides\ by\ 2\\n=499\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\subtitute:\ a_1=1;\ a_n=997;\ n=499\\\\S_{499}=\dfrac{1+997}{2}\cdot499=\dfrac{998}{2}\cdot499=499\cdot499=249,001

Answer: 1 + 3 + 5 + 7 + ... + 997 = 249,001.
You might be interested in
ms shah grades 3402 math problems during 5th period this is 54% of the total number of problems she need to grade what is the to
olga_2 [115]
The total number of problems she needs to grade is 6.
6 0
3 years ago
Last year, Maria had $10,000 to invest. She invested some of it in an account that paid 6% simple interest per year, and she inv
denis-greek [22]

Answer:

$3,000 invested at 6%

$7,000 invested at 10%

Step-by-step explanation:

Maria had total $10,000 to invest.

Let x be the amount that Maria invested initially at 6% interest rate.

0.06x

Then she invested the remaining amount at 10% interest rate.

0.10(10,000 - x)

She received a total of $880 in interest.

0.06x + 0.10(10,000 - x) = 880

0.06x + 1000 - 0.10x = 880

-0.04x = 880 - 1000

-0.04x = -120

0.04x = 120

x = 120/0.04

x = $3,000

This is the amount that Maria invested initially at 6% interest rate.

The remaining amount is

10,000 - 3,000

$7,000

This is the remaining amount that she invested at 10% interest rate.

3 0
3 years ago
Find the missing terms of the geometric sequence.
Debora [2.8K]
Funny cause I just did something similar a few minutes ago

6 0
3 years ago
How do I do this ahh!?
NISA [10]
Just scan it, there’s an answer for it already I’m pretty sure
3 0
3 years ago
How do you simplify this?<br>x²y+xy² / y²+2/5 × xy​​​
polet [3.4K]

\huge \boxed{\mathbb{QUESTION} \downarrow}

  • How do you simplify this?
  • x²y+xy² / y²+2/5 × xy

\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}

\sf\frac{  { x  }^{ 2  }  y+x { y  }^{ 2  }    }{  { y  }^{ 2  }  + \frac{ 2  }{ 5  }   \times  xy  } \\

Factor the expressions that are not already factored.

_____

<u>How </u><u>to</u><u> factorise</u><u> </u><u>:</u><u>-</u>

<u>NUMERATOR</u> \downarrow

\sf \: x ^ { 2 } y + x y ^ { 2 }

Factor out xy.

\sf \: xy\left(x+y\right)

<u>DENOMINATOR</u> \downarrow

\sf{ y  }^{ 2  }  + \frac{ 2  }{ 5  }   \times  xy \\

Factor out 1/5.

\sf \: {\frac{1}{5}y\left(2x+5y\right)}  \\

_____

Continuing...

\sf\frac{xy\left(x+y\right)}{\frac{1}{5}y\left(2x+5y\right)}  \\

Cancel out y in both the numerator and denominator.

\sf\frac{x\left(x+y\right)}{\frac{1}{5}\left(2x+5y\right)}  \\

Expand the expression.

\sf\frac{x^{2}+xy}{\frac{2}{5}x+y}  \\

This can further simplified to as \downarrow

=    \boxed{\boxed{\bf\frac{5x\left(x  +y\right)}{2x+5y}}}

3 0
3 years ago
Other questions:
  • Relate the value is between the 1s in the number 115,093,628
    10·1 answer
  • Match the cube roots and square roots with their values.
    14·1 answer
  • T(x)=1-2x how do you graph this problem
    5·1 answer
  • This is my home work plese help
    9·2 answers
  • Solve the equation.<br> F - 8/9 = 5/8<br> f = ?
    9·2 answers
  • A dance group from Round Rock High School is fundraising to travel to a competition. The competition entry fee is only $300 for
    9·1 answer
  • 9 divided by 4 as a mixed number
    6·2 answers
  • What is 12.5 times 0.74 and can you please put an explanation on how to get it please
    7·2 answers
  • A stock market gains 83 points. The next day, the stock market loses 47 points.Write each amount as an interger
    6·2 answers
  • Simplify the expression please help ASAP
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!