Arithmatic Series Question

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valid

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Hi, im new to the forum and wondering if anyone could help me with a problem im having. Not sure if this is the right forum to post this in, if not please let me know and I will delete and repost.

I've got an arithmetic progression question that im struggling with.

I need to transpose the formula Sn=n/2(2a+(n-1)) for n

I know a=150, d=200 and Sn=1296000.

ive tried all sorts of ways but cant manage it

thanks

J
 
valid said:
Hi, im new to the forum and wondering if anyone could help me with a problem im having. Not sure if this is the right forum to post this in, if not please let me know and I will delete and repost.

I've got an arithmetic progression question that im struggling with.

I need to transpose the formula Sn=n/2(2a+(n-1)) for n

I know a=150, d=200 and Sn=1296000.

ive tried all sorts of ways but cant manage it

thanks

J
Click to expand...
First I don't see a 'd'. However, knowing everything but n in the equation, you have a simple equation for n. Depending on just what the formula is we have either a linear equation or a quadratic equation or a ... in n. Assume the equation is
Sn = (n / 2) (2a + (n-1))
then, multiplying through by 2 and distributing the n through we have
2 Sn = n2 + (2a-1) n
or
n2 + (2a-1) n - 2 Sn = 0
which is a quadratic equation in n. Looking at it, it has two real roots; one negative and one positive. I would assume you would want the positive root but maybe not.

On the other hand, if the equation was
Sn = n / [ 2 (2a + (n-1)) ]
you could multiply through by the denominator and get a linear equation in n with just 1 solution.
 
Thanks very much for the help. Much appreciated, and yes, I forgot to include d in the original equations

Cheers
 
So basically, when given a problem of that type, you should state that the formula needs re-arranging, so to work out the quadratic formula?
 
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