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
umka2103 [35]
3 years ago
10

The set of the consecutive odd numbers 1, 3, 5, 7, ... , N has a sum of 400. How many numbers are in the set?

Mathematics
1 answer:
Amanda [17]3 years ago
3 0

Well, we could try adding up odd numbers, and look to see when we reach 400. But I'm hoping to find an easier way.

First of all ... I'm not sure this will help, but let's stop and notice it anyway ...
An odd number of odd numbers (like 1, 3, 5) add up to an odd number, but
an even number of odd numbers (like 1,3,5,7) add up to an even number.
So if the sum is going to be exactly 400, then there will have to be an even
number of items in the set.

Now, let's put down an even number of odd numbers to work with,and see
what we can notice about them:

         1, 3, 5, 7, 9, 11, 13, 15 .

Number of items in the set . . . 8
Sum of all the items in the set . . . 64

Hmmm.  That's interesting.  64 happens to be the square of 8 . 
Do you think that might be all there is to it ?

Let's check it out:

Even-numbered lists of odd numbers:

1, 3                                   Items = 2, Sum = 4
1, 3, 5, 7                           Items = 4, Sum = 16
1, 3, 5, 7, 9, 11                 Items = 6, Sum = 36
1, 3, 5, 7, 9, 11, 13, 15 . . Items = 8, Sum = 64 .

Amazing !  The sum is always the square of the number of items in the set !

For a sum of 400 ... which just happens to be the square of 20,
we just need the <em><u>first 20 consecutive odd numbers</u></em>.

I slogged through it on my calculator, and it's true.

I never knew this before.  It seems to be something valuable
to keep in my tool-box (and cherish always).


You might be interested in
21 x ________ ÷ 3 = 21 *
GrogVix [38]

Answer:

first one: <u>3</u>

second one: <u>b</u>

third one: <u>3.2</u>

Step-by-step explanation:

first one:

21 x ________ ÷ 3 = 21

rewrite equation:

21 ÷ 3 x ___ = 21

7 x ___ = 21

(21 / 7 = 3)

7 x 3 = 21

second one:

b x h ÷ h = ___

B

third one:

876 x 3.2 ÷ ______ = 876

2803.2 ÷ ___ = 876

(2803.2 / 876 = 3.2)

2803.2 x 3.2 = 876

7 0
3 years ago
Write each of the following decimals in words.
Sergeeva-Olga [200]

A. nine hundredths

B. Thirty five hundredths

C. Seven Tenths

D. Three Thousandths

E. One Hundred Fourty five Thousandths

F. Fifty Nine Ten Thousandths

8 0
3 years ago
What is an equation of the line that passes through the point (-2,-8) and has the slope of 3
NeTakaya

Answer:

y = 3x - 2

Step-by-step explanation:

y +8 = 3 (x + 2)

y + 8 = 3x + 6

y = 3x - 2

3 0
3 years ago
Amir has RM565. He spent all his money buying b pieces of clothing which cost Rm70 per piece and k pairs of shoes which cost RM9
agasfer [191]

Answer:

70b+95k=565. I think it's like this

6 0
2 years ago
Read 2 more answers
Does 4n = -20. = -24
Arada [10]
To solve 4n you need to divide both sides by 4
8 0
3 years ago
Other questions:
  • Is Math 1 the same thing as Algebra 1?
    6·1 answer
  • Le 1
    5·1 answer
  • 1. There are 26 letters in the alphabet. If A = 1 and Z = 26, what is the sum of B and Y?
    15·2 answers
  • What is 1693 rounded to the nearest ten and hundred
    6·2 answers
  • The polygons below are similar. Find the scale factor of the SMALLER figure to the LARGER.
    15·1 answer
  • Chanise's allowance is 1 3 of her older brother's allowance. Chanise's allowance is $6 per week. Solve the equation a 3 =6 to fi
    14·1 answer
  • I need to find the measure
    8·1 answer
  • Simplify: 16 - [11 - {8+ (17 +3x2 - 19)}]
    14·1 answer
  • Angle ABF is 77
    11·1 answer
  • Lin and her friends went out for ice cream after school. The following questions came up during their trip. Select all the quest
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!