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# Can anyone do this c1 question watch

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1. Find the sum of the first 50 even numbers. (sequences)

I used the sum of natural numbers formula like this:

Sequence: 2, 4, 6......50

so: 2 ( 1, 2 , 3.....25)

{n(n+1)}/2 is 2[ {25(26)}/2 ] which is 650.

2. (Original post by littlemisshala)
Find the sum of the first 50 even numbers. (sequences)

I used the sum of natural numbers formula like this:

Sequence: 2, 4, 6......50

so: 2 ( 1, 2 , 3.....25)

{n(n+1)}/2 is 2[ {25(26)}/2 ] which is 650.

whoops

its from n = 1 to 50; you were thinking sum of even numbers from 1 to 50...
and so was I
3. (Original post by kikzen)
the answer is 650 (manually work it out if you like)... check what youre reading?
I worked it out to be 650 but the book says its 2450!!! Definite error?
4. (Original post by littlemisshala)
Find the sum of the first 50 even numbers. (sequences)

I used the sum of natural numbers formula like this:

Sequence: 2, 4, 6......50

so: 2 ( 1, 2 , 3.....25)

{n(n+1)}/2 is 2[ {25(26)}/2 ] which is 650.

even numbers can be worked out using 2n, so the last term is 100

using Sum_n=(n/2)(a+l) for arithmetic series)

a = first term = 2(1) = 2
l = last term = 2(50) = 100
n = 50

Sum_50 = (50/2)(2+100)
Sum_50 = 25*102
Sum_50 = 2550

The answer in the book suggests the first even number is 0, in which case...

a = first term = 0 = 0
l = last term = 2(49) = 98
n = 50

Sum_50 = (50/2)(0+98)
Sum_50 = 25*98
Sum_50 = 2450
5. (Original post by El Stevo)
even numbers can be worked out using 2n, so the last term is 100

using Sum_n=(n/2)(a+l) for arithmetic series)

a = first term = 2(1) = 2
l = last term = 2(50) = 100
n = 50

Sum_50 = (50/2)(2+100)
Sum_50 = 25*102
Sum_50 = 2550

The answer in the book suggests the first even number is 0, in which case...

a = first term = 0 = 0
l = last term = 2(49) = 98
n = 50

Sum_50 = (50/2)(0+98)
Sum_50 = 25*98
Sum_50 = 2450
I don't understand what you mean by 2n? Also, why do u use the above formula and not the sum of natural no.formula?
6. (Original post by littlemisshala)
I don't understand what you mean by 2n? Also, why do u use the above formula and not the sum of natural no.formula?
He used 2n because it is even numbers, ie numbers which have 2 as a factor.
So when;
n = 0, 2n = 0
n = 1, 2n = 2
n = 2, 2n = 4
n = 3, 2n = 6

e.g. even numbers.

if you wanted numbers which have 3 as a factor, you would use 3n.

If you wanted, you could derive a formula for the sum of even numbers.

Sn = n/2(2(2) + 2(n-1))
Sn = n/2(4 + 2n - 2)
Sn = n/2(2n + 2)
Sn = n^2 + n

E.g.
S4 = (4)^2 + 4 = 20

2 + 4 + 6 + 8 = 20

S7 = (7)^2 + 7 = 56

2 + 4 + 6 + 8 + 10 + 12 + 14 = 56
7. (Original post by littlemisshala)
Find the sum of the first 50 even numbers. (sequences)

I used the sum of natural numbers formula like this:

Sequence: 2, 4, 6......50

so: 2 ( 1, 2 , 3.....25)

{n(n+1)}/2 is 2[ {25(26)}/2 ] which is 650.

El stevo is right.
the question ask SUM OF FIRST 50 EVEN NUMBER,
50 IS THE 26TH EVEN UUMBER,98 IS THE 50TH
8. Sequence 0,2,4,6,8 etc..

Sn=n x (a+l)/2

a=2
l=98
n=50

S50=50 x (98+0)/2
S50=50 x 49
S50=2450.
9. use the formula : Sn = n/2 (2a + (n-1)d))
where
n=50
a=0
d=2

s50= 50/2 (2x0 +(50-1)2))

S50= 25 x 98 = 2450

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Updated: January 3, 2005
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