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# AS Maths C1 Series and Sequences Help Needed Watch

1. Hi guys, I have been stuck on this particular series and sequences question for a long time and I was wondering if any of you are able to work out this question for me and show me working out as well. Thanks;
The question is:
The sum of the first 6 terms of an arithmetic series is 21, and the seventh term is three times the sum of the third and the fourth.
Find the first term and the common difference.

Any light you can shed on this on working it out would be of great help, Thanks
2. The first six terms can be written: a, a + d, a + 2d, a + 3d, a + 4d, a +5 d, where a is the first term and d is the common difference. You know that if you add all of these up, you get 21.

The seventh term is a + 6d, and the sum of the third and the fourth is (a + 2d) + (a + 3d).

Can you now use the information in the question to set up two simultaneous equations for a and d? And then solve them?
3. I have found the values of a and d (the first term and common difference). Have you attempted to solve it?
4. ans: a = 3 , d = 3

did you get this?
5. (Original post by ilyking)
ans: a = 3 , d = 3

did you get this?
Incorrect. This is because the sequence will go: 3,6,9,12.. etc. The sum of the first 6 terms is 21 remember.

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