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Find the first term & common difference if:
1) 10th term is 35; 15th terms is 55
2) 2nd term is 56 ; 12th term is 16
3) 8th term is 4; 18th term is -96
4) 7th term is -25; 2th term is -45
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I will solve #1 only. Do the remaining cases following the same pattern.
1) 10th term is 35; 15th terms is 55.
Between the 10-th and 15-th terms, there is the room for 5 (=15-10) common differences d.
So, 5d = 55 - 35 = 20. Hence, d = = 4.
Thus you just found the common difference d = 4.
Then from = + 9*d you have
= - 9d = 35 - 9*4 = 35 - 36 = -1.
Answer. = -1; d = 4.
Make the remaining cases following this pattern.
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".