A level the sum of an Arithmetic Progression, find a and d

Hi there

I am unsure how to get the answer for this question:

Q: The sum of the first n terms of an Arithmetic Progression, Sn, is n(n-2).
Find a and d.

a = the first term
d = the common difference

I tried subsituting an actual number for n twice, then solved the simultaneous equations, but I didn't get the same answers in the book, which are:

A: a = -1 and d = 2

Can anyone help me?

Many thanks
Jackie

Reply 1

steve2005

17

Original post by jackie11

Hi there

I am unsure how to get the answer for this question:

Q: The sum of the first n terms of an Arithmetic Progression, Sn, is n(n-2).
Find a and d.

a = the first term
d = the common difference

I tried subsituting an actual number for n twice, then solved the simultaneous equations, but I didn't get the same answers in the book, which are:

A: a = -1 and d = 2

Can anyone help me?

Many thanks
Jackie

Sum of AP = (n/2)(2a+(n-1)d)

Reply 2

username667907

4

S_n = \frac{1}{2} n \left[ \ 2a+ (n-1) d\ \right]

Reply 3

TenOfThem

18

You know what a is since the sum of the first 1 term is 1(1-2)

Then you can find the second term because the sum of the first 2 terms is 2(2-2)

Reply 4

jackie11

OP

4

aww Thank you, I've got it.

s1 = 1 (1-2)
s1 = -1
so a = -1

s2 = 2 (2-2)
s2 = 2 x 0
s2 = 0

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

0 = 1/2(2) [2(-1) + (2-1)d]

0 = 1 [-2 + (1 x d)]

0 = -2 + (1 x d)

0 = -2 + 2 which = 0

so d must be 2

yay!!!! :smile:

thank you all

A level the sum of an Arithmetic Progression, find a and d

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