.
Between the 6th and 4th terms of an AP there is the room for two common differencies;
therefore, the common difference d = = = 9.
In more formal way, = - = 2d = 24 - 6 = 18, hence, d = = 9.
Then = = 6 - 3*9 = -21.
As you know now and d, you actually know EVERYTHING about the given AP.
For example, = = -21 + 6*9 = 33.
Now, the sum of the first 7 terms is = = = 42.
= = -21+ 7*9 = 42.
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There is a bunch of lessons on arithmetic progressions in this site:
- Arithmetic progressions
- The proofs of the formulas for arithmetic progressions
- Problems on arithmetic progressions
- Word problems on arithmetic progressions
- Mathematical induction and arithmetic progressions
- One characteristic property of arithmetic progressions
- Solved problems on arithmetic progressions
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.