Arithmetic sequences, just a quick question :)

[alyson]

hello, i have this maths question that i feel like i should be able to do easily but i cant
its arithmetic progressions, and the question is to find the sum of the first 8 digits, where the first two are the sum of 18, and the first four are the sum of 52
please could someone just help me work out, I'm not asking for all the work to do just the method needed so i can follow it and get the answer, which btw is 168 as it says in the back of my book, many thanks,

 

[galactus]

Try this one:

7+11+15+19+......

7+11=18 and 7+11+15+19=52

Continue on.

Remember, the nth partial sum of an arithmetic series is \(\displaystyle S_{n}=\frac{n}{2}(a_{1}+a_{n})\)

You are given \(\displaystyle S_{2}=a_{1}+a_{2}\) and \(\displaystyle S_{4}=2(a_{1}+a_{4})\)

You need \(\displaystyle S_{8}=4(a_{1}+a_{8})\)