Question

HELLLP!

Answer 1

1. What is the sum of the multiples of 4 from 16 to 100? (1 point)

Answer 2

I would write down
4+8+12+ 16+ .... + 100
then factor out a four from each term:
4(1+2+3+...+25)

however they want from 16 to 100:
4(4+5+6+...25)= 4( 1+2+...+25) - 4(1+2+3)

the sum of the numbers from 1 to 25 is ?

Answer 3

25?

Answer 4

1+2+3+4+...+24+25 is not 25

have you seen n*(n+1)/2 formula ?

Answer 5

no i havent

Answer 6

is it 1,218

Answer 7

@phi?

Answer 8

See http://www.wikihow.com/Sum-the-Integers-from-1-to-N

I was looking for a web site that explained it clearly.

the sum from 1 to 25 is 25*26/2 = 25*13=

Answer 9

325?

Answer 10

I m confused

Answer 11

sum 1:25 is 325

but you want the sum from 4:25, so subtract off 1+2+3
we can do that in our head: 6
or using the formula: 3*4/2 =3*2= 6

the sum 4:25 is 325-6= 219

now multiply by 4 because we want 4*(4+5+6...+25)

Answer 12

yes, it is confusing, because we are doing a bunch of different things.

Answer 13

no thats not it

Answer 14

is the answer 1,300

Answer 15

Let's start at the beginning, and do it step by step.

The first thing I thought was write down the multiplies of 4
4+8+12+16+ ... + 100

do you see you can factor 4 out of each number to get:
4* (1+2+3+4...+25) ?

Answer 16

yeah

Answer 17

now we can use the formula to find what number that mess adds up to:
if you add up 1+2+3+... +25 you get 325 (using 25*26/2 )

Answer 18

yeah i see

Answer 19

so we know so far
4* (1+2+3+4...+25) = 325

Answer 20

yup i see it

Answer 21

but that is not what they want to know.
however, we can write
4* (1+2+3+4...+25) = 325
as
4*( (1+2+3) + (4+5+6+...+25)) = 325

I put parens around the 1+2+3 and parens around the rest.

Answer 22

ok..

Answer 23

4*( (1+2+3) + (4+5+6+...+25)) = 325
now "distribute the 4
4*(1+2+3) + 4*(4+5+...+25) = 325

the second part is what we want: 4(4+5+6...+25) is 16+20+24...+100

Answer 24

im with you

Answer 25

I just noticed I left out a 4!

I started with
1+2+3+... +25 = 325

then I multiplied BOTH sides by 4 to get
4*(1+2+3+... +25 ) = 4*325
so those other posts should show 4*325 on the right side not just 325

subtract 4*(1+2+3) from both sides
4*(1+2+3) + 4*(4+5+...+25) = 4*325
to get
4*(4+5+...+25) = 4*325- 4*(1+2+3)

the left side is what we want. the right side will be a number: 4*325-4*6

Answer 26

ok i see

Answer 27

whats the next step

Answer 28

4*(4+5+...+25) = 4*325- 4*(1+2+3)

the left side is what we want. the right side will be a number: 4*325-4*6

Answer 29

oh ok so the other way around

Answer 30

in other words
4*(4+5+...+25) = 4*325- 4*(1+2+3)
or, distributing the 4,

16+20+24+...+100= 4*325-4*(1+2+3)

Answer 31

you can figure out what 4*325-4*(1+2+3) is, right ?

Answer 32

ok