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C1- Sequences - sum of question type?

How do you answer part D? Can someone explain please.
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You can't use the formula and its too much to work out without any sort of technique :s-smilie:
The first thing you should know is that its a series
Its the sum of the series from 1 to 100 so x1+ x2+ x3 + ... + x100 and just use the formula in the formula book to work it out
Reply 3
Original post by SalazarSlytherin
Its the sum of the series from 1 to 100 so x1+ x2+ x3 + ... + x100 and just use the formula in the formula book to work it out

Isn't it the formula for arithmetic series only? If the difference is the same?
Reply 4
Original post by Questioness
How do you answer part D? Can someone explain please.
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You can't use the formula and its too much to work out without any sort of technique :s-smilie:


Write out the values of x1,x2,x3,x4,x5,x6,x7,x8,x9x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9 and see if you notice some sort of pattern...
Original post by Questioness
How do you answer part D? Can someone explain please.
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You can't use the formula and its too much to work out without any sort of technique :s-smilie:


Write out the first four or so terms. You should see a simple pattern.
Reply 6
Original post by SalazarSlytherin
Its the sum of the series from 1 to 100 so x1+ x2+ x3 + ... + x100 and just use the formula in the formula book to work it out


Original post by XOR_
a = 1 = x1, find d (common difference) and use sn=(n/2)(2a+(n-1)d)


It's not an arithmetic series. (as can be seen multiple times throughout the question).
Reply 7
Original post by Zacken
It's not an arithmetic series. (as can be seen multiple times throughout the question).


So it is either equal to -1/2 or 1. How exactly do I work it out?
(1*50) + (1/2 * 50) = 75
Reply 9
Original post by Questioness
So it is either equal to -1/2 or 1. How exactly do I work it out?


Are you sure it's -1/2? If so, just replace my thing below with (1+1+ + ... ) -(1/2 + 1/2+ 1/2 + ... + 1/2) instead

Anyways, if you're adding up 1 + 1/2 + 1 + 1/2 + ... 100 times, you can just split it into (1+1+1+...+1) + (1/2 + 1/2+1/2+1/2) 50 times each.

Adding the same thing up a number of times has a name, it's called multiplication. So 1 + 1 + 1 + ... + 1 50 times is 1 * 50.

(just check whether it's -1/2 or +1/2)
Original post by Questioness
So it is either equal to -1/2 or 1. How exactly do I work it out?


It's equal to some 1s added together plus some -1/2s added together. How many of each do you have?
Reply 11
You found out that k is 3/2.

So if you look at the first 4 terms, you can clearly see a pattern of 1, -1/2, 1, -1/2 and so on.

You need the sum of the first 100 terms. Which means, a half of those will be 1s, and the other half will be -1/2s. Thus, 50*1+50*(-1/2)=50-25=25.
Reply 12
Original post by morgan8002
It's equal to some 1s added together plus some -1/2s added together. How many of each do you have?


Original post by pecora
You found out that k is 3/2.

So if you look at the first 4 terms, you can clearly see a pattern of 1, -1/2, 1, -1/2 and so on.

You need the sum of the first 100 terms. Which means, a half of those will be 1s, and the other half will be -1/2s. Thus, 50*1+50*(-1/2)=50-25=25.


Original post by Zacken
Are you sure it's -1/2? If so, just replace my thing below with (1+1+ + ... ) -(1/2 + 1/2+ 1/2 + ... + 1/2) instead

Anyways, if you're adding up 1 + 1/2 + 1 + 1/2 + ... 100 times, you can just split it into (1+1+1+...+1) + (1/2 + 1/2+1/2+1/2) 50 times each.

Adding the same thing up a number of times has a name, it's called multiplication. So 1 + 1 + 1 + ... + 1 50 times is 1 * 50.

(just check whether it's -1/2 or +1/2)


Thanks!! :biggrin: . I understand now.

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