sum of an arithmetic series ...
you know , , and ... so, what's the problem with finding ?
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.
Hello, parad80!
You say you understand the formulas.
I don't understand your difficulty.
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.
The sum is the first n terms of an arithmetic series: .
We are given: .
We have: .
2. The first term of an arithmetic series is 16.
The 30th term is 100.
Calculate S30
We are given: .
We have: .
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
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.
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
With regard to the second question:
I have the following formula:The first term of an arithmetic series is 16. The 30th term is 100. Calculate S30
so
and
Where from here? Can't help feeling I am going about this in the wrong way.
PD
Got it - thanks.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.)