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
kirill [66]
3 years ago
11

What is the sum of the first 70 consecutive odd numbers? Explain.

Mathematics
1 answer:
expeople1 [14]3 years ago
5 0

The sum of the first n odd numbers is n squared! So, the short answer is that the sum of the first 70 odd numbers is 70 squared, i.e. 4900.

Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.

So, if we sum the first N odd numbers, we have

\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1

The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have

\displaystyle 2\sum_{i=1}^N i = 2\cdot\dfrac{N(N+1)}{2}=N(N+1)

The second sum is simply the sum of N ones:

\underbrace{1+1+1\ldots+1}_{N\text{ times}}=N

So, the final result is

\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1 = N(N+1)-N = N^2+N-N = N^2

which ends the proof.

You might be interested in
Crystal earns $5.50 per hours mowing lawns. Write a rule to describe how the amout of money m earned is a function of the number
ra1l [238]
She earns $5.50 for every hour so:
m = 5.5h
3 hours and 45 minutes is 3.75 hours.
m = 5.5(3.75)
m = 20.625
After rounding, she earns $20.63.
4 0
3 years ago
Reynaldo rode his bike 2 miles north and 3 miles east. Which equation should he ise to find the distance, d, that takes him dire
ValentinkaMS [17]
Pythagorean theorem - a^2 + b^2 = c^2

2^2+3^2 = d^2
d^2 = 13
d= square root of 13
6 0
3 years ago
Read 3 more answers
HELLLLPPPPPLPPOOLL no fake answers pls
stepan [7]

Answer:

x = 11

Step-by-step explanation:

(3x + 28) + (5x + 52) + ( 2x - 10) = 180

(3x + 5x + 2x) + (28 + 52 - 10) = 180

10x + 70 = 180

10x = 180 - 70

10x = 110

x = 11

6 0
3 years ago
Read 2 more answers
What’s is 63 fl oz;7 c; and 1.5 qt from least to greatest
Snowcat [4.5K]

Step-by-step explanation:

explain what 7 c is please and I'll write the answer in the comments:))

8 0
3 years ago
Mrs. Jackson put a total of $10,000 into two accounts one account earns 6% simple annual interest the other account earns 6.5% s
kozerog [31]

Answer:

The money invested in account at 6 % rate is $ 9230.77

The money invested in account at 6.5 % rate is $ 769.23

Step-by-step explanation:

Given as :

The total amount saves in two account = $ 10,000

The two rate of interest are 6 % and 6.5 % at simple interest

The interest earn at 6 % rate = $ 632

The interest earn at 6.5 % ate = $ 50

Now, Let The amount deposit at 6 % rate = $ x

And The amount deposit at 6.5 % rate = $ 10,000 - $ x

<u>From Simple Interest method</u>

Simple Interest = \dfrac{\textrm principal \times \textrm Rate\times \textrm time}{100}

or, At 6.5 % rate

$ 50 =  \dfrac{\textrm (10,000 - x ) \times \textrm 6.5\times \textrm 1}{100}

or, 10000 - x =  \frac{5000}{6.5}

Or, 10000 - x = 769.23

∴  x = 10000 - 769.23

I.e x = $ 9230.77

So , At 6.5 % the amount deposit = 10,000 - 9230.77 = $ 769.23

So, At 6 % The amount deposit  = $ 9230.77

Hence The money invested in account at 6 % rate is $ 9230.77

And  The money invested in account at 6.5 % rate is $ 769.23 Answer

7 0
3 years ago
Other questions:
  • The graph that is made up of two straight lines, which has an absolute maximum or absolute minimum, and is symmetric belongs to
    13·1 answer
  • X2 + 1+ x – 2 what is the answer
    10·2 answers
  • Solve the equation for the letter d: C=pi*d<br>  Pleaseeee someone help me
    7·1 answer
  • What is the value of x:
    8·1 answer
  • You spending $144 for new sweaters,T-Shirts and pants.Sweaters cost $28,T-Shirts (t) cost $14 and pants (p) cost $23,each.Which
    11·1 answer
  • Help me plzzz with my hw
    6·1 answer
  • In the figure below, PEZS. What is the value of x?<br> P<br> 7x+4<br> 6x+8<br> T<br> 5x+10<br> S
    10·1 answer
  • A rectangular prism has the following dimensions.
    12·2 answers
  • I need to find the area. (please help me quick &amp; the answer and explanation plz) POINTS: 15! please give real answers!!!!
    6·2 answers
  • Whats the value of -6​
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!