.
= a + 41*d = 194. (1)
= a + 87*d = 424. (2)
The unknown "a" is the first term, and the unknown "d" is the common difference of the AP.
Thus you have the system of 2 linear equations in 2 unknown, so it is solvable.
The easiest way to solve it is to subtract equation (1) from equation (2). You will get
87d - 41d = 424 - 194
46d = 230
d = 230/46 = 5.
Then from equation (1), a = 194 - 5*41 = -11.
Now you know EVERYTHING about your AP. In particular,
= a + 5*9 = -11 + 45 = 34. ANSWER
Solved.
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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
- One characteristic property of arithmetic progressions
- Solved problems on arithmetic progressions
- Calculating partial sums of arithmetic progressions
- Mathematical induction and arithmetic progressions
- Mathematical induction for sequences other than arithmetic or geometric
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.
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