Finding the first term/common difference of an arithmetic series with 2 sums

[sam1]

Hello,

I'm struggling with this question. Any help and I'd be so thankful.
I've tried using the formula: Sn = 1/2n (2a1 + d(n-1))
but I'm stuck.

The sum of the first four terms is 38.
The sum of the same series to 8 terms is 124.
Find the first term and common difference.


​Thanks

 

[tkhunny]

What you are saying is that you have no idea how the formula works.

Please tell me what \(\displaystyle S_{2}\) means.

 

[mmm4444bot]

I've tried using the formula: Sn = 1/2 n (2a + d(n-1))
but I'm stuck.

Please show us what you tried, so that we can see where you're stuck. :cool:

 

[stapel]

I've tried using the formula \(\displaystyle S_n\, =\, \dfrac{n}{2}\, \big(2a_1\, +\, d\, (n\, -\, 1)\big)\) but I'm stuck.

The sum of the first four terms is 38.
The sum of the same series to 8 terms is 124.
Find the first term and common difference.

What did you get when you plugged the given information into the specified formula? What did you get when you simplified each of the two equations? When you subtracted the first equation from the second equation, what did you get at the value for "d"? When you plugged this value back into either of the original two equations, what did you get for the value of the first term?

Please be complete. Thank you!