Find the sum of Natural Numbers from 1 to 200 excluding those divisible by 5?

Question

Solve The Question in complete Detail.
And Please Dont Tell Me To My Own Homework cuz This Sum s The Only Sum That I Keep Goin Wrong In

Answer 1

I guess you know how to find the sum of numbers. Think of this as two series.

1,2,3,4 ......200 you can calculate the sum of this

200/2 * (1+200) = 20100


The next series is
5,10,15 .... 200 (all the numbers divisible by 5) the sum of this is

40/2 * (200+5) = 4100

So the required total = 20100-4100 = 16000

Answer 2

Sum of numbers from 1 to 200 is
1+2+3+4+....... +200 = (200(200+1)/2)*1
= 20100

Sum of numbers divisible by 5 from 1 to 200
5+10+15..........+200 = (40(40+1)/2)*5
= 4100

Sum of natural numbers from 1 to 200 excluding those divisible by 5 = 20100 - 4100 = 16000

Answer 3

Let
s = the sum of Natural Numbers from 1 to 200 excluding those divisible by 5
t = the sum of Natural Numbers from 1 to 200 which are divisible by 5
u = the sum of Natural Numbers from 1 to 200

From the variables (and by common sense),
s = u - t

Given the arithmetic series formula
s_n = n(a_1 + a_n)/2

and the arithmetic sequence formula
a_n = a_1 + (n - 1)d

solving for n,
a_n - a_1 = (n - 1)d
n - 1 = (a_n - a_1)/d
n = (a_n - a_1)/d + 1

for t(sum of numbers fr. 1 to 200 div. by 5)
a_n = 200
a_1 = 5
d = 5
n = (200 - 5)/5 + 1
n = 40 - 1 + 1
n = 40
s_n = t = 40(5 + 195)/2
t = 40(200)/2
t = 4000

for u (sum of natural numbers fr. 1 to 200)
a_1 = 1
a_n = 200
d = 1
n = (200 - 1)/1 + 1
n = 200 - 1 + 1
n = 200
s_n = u = 200(1 + 200)/2
u = 100(201)
u = 20100

Thus,
s = u - t
s = 20100 - 4000
s = 16100

.·. the sum of the natural numbers from 1 to 200 excluding those which are divisible by 5 is 16,100. ^_^
^_^

Answer 4

it can be written like this:
(1+2+3+...+100) - (5+10+15+...+100)
=(1+2+3+...+100) - (5(1+2+3+...20))

the sum of the first n natural numbers = (n)(n+1)/2

so, the sum of the first 100 natural numbers (1+2+3+...100)
= (100)(100+1)/2
= (100)(101)/2
= 5050
and the sum of the first 20 natural numbers (1+2+3+...+20)
=(20)(20+1)/2
= (20)(21)/2
= 210

so,
(1+2+3+...+100) - (5(1+2+3+...+20))
= 5050 - (5)(210)
= 5050 - 1050
= 4000

Answer 5

200 * (200 + 1) / 2 -

200 * (200 + 1) / (2 * 5)

(this only works if 200 is divisible by 5, otherwise you have to add or subtract 1)

Answer 6

I received Tongues and Interpretation in English. It came naturally that I doubted it. A Indian lady asked me to pray for her and English came out. I was ashamed or did not want to seem weird. She later told me it was true. Do I believe the gift is genuine? I can have a word come out...but I would not dare go on youtube. I am not that confident. Perhaps that is what started me on a quest... I believe in the gifts and I received the Baptism of the Holy Spirit.

Answer 7

16000