The sum of the first 20 terms of an arithmetic sequence isp, and the sum of the first 22 isq. Write down expressions for the common difference, and the sum of the first 18 terms.

Thanks!

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- May 3rd 2013, 06:52 PMlolylandArithmetic Sequences
The sum of the first 20 terms of an arithmetic sequence is

*p*, and the sum of the first 22 is**q**. Write down expressions for the common difference, and the sum of the first 18 terms.

Thanks! - May 3rd 2013, 08:11 PMProve ItRe: Arithmetic Sequences
For starters, can you set up two equations from the two first two bits of information?

- May 3rd 2013, 10:54 PMlolylandRe: Arithmetic Sequences
S2o=p

S22=q - May 3rd 2013, 11:46 PMibduttRe: Arithmetic Sequences
Remember nth term of an AP is given by = a + ( n-1) d where a is the first term and d the common difference.

Thus you have

a + 21 d = q and a + 19d = p

I am sure now you know what to do further - May 4th 2013, 02:27 AMlolylandRe: Arithmetic Sequences
I know you have to use the equation: Sn= n/2 (a+ (n-1) d)

I'm still so confused, sorry!! - May 5th 2013, 09:32 PMibduttRe: Arithmetic Sequences
That is right, The formula for the sum of n terms of an AP is Sn= n/2 [ 2a + ( n-1) d ] Note that it should be 2a and not a.

So there is nothing left for now you have

10 [ 2a+19 d ] = p and 11 [ 2a + 21 d ] = q. now find a the first term and d the common difference and get the result.