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C1 sequences and series question

need help

An arithmitic series has first term a and common difference d.

a) Prove that the sum of the first n terms of the series is:

1/2n[2a+(n-1)d]

I actually dont understand how to do this :s-smilie:
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Avatar for jamestg
jamestg
21
Original post by SuperHuman98
need help

An arithmitic series has first term a and common difference d.

a) Prove that the sum of the first n terms of the series is:

1/2n[2a+(n-1)d]

I actually dont understand how to do this :s-smilie:


it's n/2, not 1/2n :smile:

Think back to arithmetic progression

Sn = a + a+d + a+2d + a+3d... a+(n-1)d
Sn= a+(n-1)d... a+3d (etc)

2Sn = n[a+a+(n-1)d]
Sn = (n/2)[2a+(n-1)d]
Original post by jamestg
it's n/2, not 1/2n :smile:

Think back to arithmetic progression

Sn = a + a+d + a+2d + a+3d... a+(n-1)d
Sn= a+(n-1)d... a+3d (etc)

2Sn = n[a+a+(n-1)d]
Sn = (n/2)[2a+(n-1)d]


the question says 1/2n
Reply 3
Avatar for jamestg
jamestg
21
Original post by SuperHuman98
the question says 1/2n

It's a typo the sum of an arithmetic progression has the formula with n/2 not 1/2n

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