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Mathematics
OpenStudy (anonymous):

The sum of all odd numbers form 1 to 99 is?

OpenStudy (anonymous):

use sum of aritmetic sequence. .

Parth (parthkohli):

1 + 3 + 5 + 7.....But you need not do that since it is an arithmetic sequence.

Parth (parthkohli):

The sum of an arithmetic sequence is: \(\Large \color{Black}{\Rightarrow {n \over 2}(a_1 + a_l) }\) a1 is the first term aL is the last n is the number of terms

OpenStudy (anonymous):

After 1 add? Should i cross multiply?

Parth (parthkohli):

1st term is 1. Last is 99. Odd numbers between 1,100 are 50.

Parth (parthkohli):

The common difference is d, btw.

OpenStudy (anonymous):

@ParthKohli , i think you've mistaken the formula. . http://www.regentsprep.org/Regents/math/algtrig/ATP2/ArithSeq.htm

Parth (parthkohli):

Oops, it was aN lol

OpenStudy (anonymous):

it's ok. .

OpenStudy (anonymous):

I dont get it XD

Parth (parthkohli):

Hey I know another pattern.

Parth (parthkohli):

The sum of first n odd numbers is n squared. The sum of first 50 odd numbers is 50 squared. So, 50^2 = 2500

Parth (parthkohli):

Well actually my formula was correct.

Parth (parthkohli):

I learnt this pattern at school.

OpenStudy (anonymous):

Ca you give me an example?

Parth (parthkohli):

For example the sum of first 4 odd numbers is 4 squared aka 16 1 + 3 + 5 + 7 = 4 + 12 = 16

OpenStudy (anonymous):

how did you got that formula? @ParthKohli

Parth (parthkohli):

Oh wait a second

Parth (parthkohli):

Yes....yes I'm correct.

OpenStudy (anonymous):

the answer is 2500, and you're correct, but how did you get that another formula?

Parth (parthkohli):

I learnt that at school

Parth (parthkohli):

@sel126 Got it?

OpenStudy (anonymous):

Yessss :) Thankyousomuch:)))))))

Parth (parthkohli):

Yw :D

OpenStudy (anonymous):

99 = a + (n-1)d hence 99 = 1 +(n-1)*3 n= 50 substituting value of n in equation S= n/2 [ 2a + (n-1)*d] we get sum of odd terms that is equal to 2500 where a =1(first term) and d =3(common difference)

OpenStudy (anonymous):

Why does three become the d?

OpenStudy (anonymous):

the sum of odd numbers is a perfect square

Parth (parthkohli):

That's what I said above

Parth (parthkohli):

Hehe don't waste your energy, genius. I've explained her.

OpenStudy (anonymous):

just thought i would mention it. no need for a formula, or all that other business, only need to know how many numbers are being added

Parth (parthkohli):

Hmm I said the exact same thing.

Parth (parthkohli):

Still here you have a medal

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