.
The MENTAL solution by the "guessing method"
= 1;
= 3;
d = 2 (the common difference);
Check: = + d*(10-1) = 1 + 2*9 = 19 ! Correct !
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= 1 + 4*2 = 9;
= 1 + 5*2 = 11;
+ = 9 + 11 = 20.
Solved.
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Surely, it can be solved algebraically
+ = 4, (1)
= = 19, (2)
which gives you the system of two equations in two unknowns
= 4,
= 19,
You can solve it by any method you know/you want to get the same answer.
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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
- 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.