Arithmetic series - stuck!

Hi all, just joined and introduced myself in the lobby.

I have two questions which I have not been able to do the workings out for. I understand the formula to calculate arithmetic series, but I am stumped on these - hope you can help.

1. The sum of an arithmetic series is 270. The common difference is 1 and the first term is 4. Calculate the number of terms in the series.

2. The first term of an arithmetic series is 16. The 30th term is 100. Calculate S30.

Can anybody show me the process they would go through?

Thanks

Parad80.

Re: Arithmetic series - stuck!

sum of an arithmetic series ...

you know , , and ... so, what's the problem with finding ?

Re: Arithmetic series - stuck!

Re: Arithmetic series - stuck!

Quote:

Originally Posted by

**skeeter** sum of an arithmetic series ...

... nope, thinking sum, putting down nth term. no more drinking and deriving.

mea culpa.

Re: Arithmetic series - stuck!

Thanks for your responses:

Don't know how you write your formula's in that font, but I understand it up to this point:

1.

n/2(8+(n-1)1),

n/2(8+(n-1)) = 270

Then what is the next step?

Thanks for your patience!

PD

Re: Arithmetic series - stuck!

expand out the brackets and use the quadratic formula.

now use the quadratic formula

remember the quadratic formula will give you two solutions, only the positive one is a feasible answer.

Re: Arithmetic series - stuck!

thanks Iinalg123

understand up to 7n+n2=540

couldn't you then divide by 7 on both sides?

With n2 + 7n - 540 is there an easy way to work the quadratic formula out?

Can someone please tell me how to write the formula's in the fonts above - thanks.

PD

Re: Arithmetic series - stuck!

Lets say you have a quadratic

the quadratic formula says the solutions are

If you use this formula for your quadratic you will get your solution for x.

Re: Arithmetic series - stuck!

ok, so I have the following:

-7 + SQRT 7 squared - 4(1)(540)

divided by

2(1)

Then:

-7 + SQRT 49 -2160

divided by

2

Then:

-7 + SQRT - 2111

divided by

2

Then:

-7 + 45.95

divided by

2

Then:

38.95

divided by

2

Then:

19.475, which rounded up is 20, which is the text book answer - thank you.

Re: Arithmetic series - stuck!

Close, however you didn't convert it to the form , you used

So, if we convert it first we have (note the negative sign for c)

So,

i.e (note the sign chance as negative * negative is positive.)

now as we only considering the positive answer

Re: Arithmetic series - stuck!

Re: Arithmetic series - stuck!

Quote:

Close, however you didn't convert it to the form. If we convert it first we have (note the negative sign for c)

i.e (note the sign chance as negative * negative is positive.)

Got it - thanks.