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It is known that {an} is an arithmetic sequence, A1 = 2, A2 = 3. If three numbers are inserted between every two adjacent terms to form a new arithmetic sequence with the number of the original sequence, we can find: (1) what is the 12th term of the original sequence? (2) What is the 29th item of the new sequence?
(1) A {an} is an arithmetic sequence, A1 = 2, A2 = 3. If three numbers are inserted between every two adjacent terms to form a new arithmetic sequence with the number of the original sequence, it can be recorded as {BN}, then the arithmetic sequence {BN} is a sequence with 2 as the first term and 3 as the fifth term. Let the tolerance of {an} be D, and let the tolerance of {BN} be d ', then 2 + D = 3, 2 + 4D ′ = 3, and the solution is d = 1, D ′ = 14, so the general term of the original arithmetic sequence {an} is : an = 2 + 1 × (n-1) = n + 1, the general term of the new arithmetic sequence {BN} is: BN = 2 + 14 (n − 1) = n + 74, so the 12th term of the original sequence is A12 = 13, let BN = 13, solve N = 45, so the 12th term of the original sequence is the 45th term of the new sequence. (2) from (1), we know that the 29th term of the new sequence is B29 = 29 + 74 = 9, let an = 9 solve N = 8, so the 29th term of the new sequence is the 8th term of the original sequence
RELATED INFORMATIONS
- 1. If the sum of their first n terms is Sn / TN = 3N + 1 / 2N-1, then the ratio of the fifth term of these two numbers is?
- 2. If the sum of the first n terms of an arithmetic sequence is 9 and the sum of the first 2n terms is 12, then the sum of the first 3N terms is?
- 3. Given that the domain of definition of function f (x) is x ∈ n * and f (x) is an increasing function, f (x) ∈ n *, f [f (n)] = 3N, find f (1) + F (2)
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- 11. In the known arithmetic sequence {an}, A1 = 2, A3 = 3, if three numbers are inserted between every two adjacent terms, it will form a new sequence with the number of the original sequence, Find 1) what is the 12th item of the original sequence? 2) whether the 29th item of the new sequence is the item of the original sequence? If so, what is it?
- 12. If the sum of the first n terms is 25 and the sum of the first 2n terms is 100, then the sum of the first 3N terms is 100______ ．
- 13. In the arithmetic sequence 2,5,8 In, three numbers are inserted between two adjacent terms to form an arithmetic sequence, so that a new sequence can be obtained In the arithmetic sequence 2,5,8 In, three numbers are inserted between each adjacent two items to form an arithmetic sequence, so as to obtain a new sequence. Question: (1) what is the 12th item of the original sequence? (2) what is the 29th item of the new sequence?
- 14. Finite sequence 1,23,26,29 Why is the number of terms of 23n + 6 N + 3
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- 16. Given that the first n terms and Sn of sequence {an} are quadratic functions of N, and its first three terms A1 = - 2, A2 = 2. A3 = 6, then A100 =?
- 17. It is known that the first n terms and Sn of sequence {an} are quadratic functions of N, and A1 = - 2, A2 = 2, A3 = 6 (1) Find Sn; (2) prove that sequence {an} is arithmetic sequence
- 18. Let {an} have 3N items in total, and the sum of the first 2n items is 100, and the sum of the last 2n items is 200. Then what is the sum of the middle n items?
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