![]() The referred lessons are the part of this online textbook under the topic "Arithmetic progressions". Solved problems on arithmetic progressionsĪlso, you have this free of charge online textbook in ALGEBRA-II in this site ![]() One characteristic property of arithmetic progressions Mathematical induction and arithmetic progressions Word problems on arithmetic progressions The proofs of the formulas for arithmetic progressions There is a bunch of lessons on arithmetic progressions in this site: Increments of a quadratic function form an arithmetic progression Uniformly accelerated motions and arithmetic progressions Then the original sequence is a quadratic sequence. If the first difference of a sequence is an arithmetic sequence, Given that the 5th term of the sequence is 40, you can find the 6th term by adding the known difference between the 5th and 6th terms and you can find the 4th, 3rd, 2nd, and 1st terms by working backwards, subtracting the known differences between terms. To get the 3rd through 6th terms, simply add the given differences between terms, as demonstrated in part A.Ĭ. ![]() If the sum of the first two terms is 11, and we know that the difference between the first two terms is 3, then we know the first two terms are 4 and 7. If the first term of the sequence is 3, then the 2nd is 3+3 = 6 the 3rd is 6+5 = 11 the 4th is 11+7 = 18 the 5th is 18+9 = 27, and the 6th is 27+11 = 38.ī. meansģ is the difference between the 1st and 2nd terms ĥ is the difference between the 2nd and 3rd terms ħ is the difference between the 3rd and 4th terms ĩ is the difference between the 4th and 5th terms andġ1 is the difference between the 5th and 6th termsĪ. The first differences being 3, 5, 7, 9, 11. This should be pretty straightforward, if you understand what the first differences of a sequence mean. You can put this solution on YOUR website!
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