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It is known that the arithmetic sequence {an} satisfies the following conditions: A3 + A4 = 16, A4 + A5 = 20, and the sum of the first n terms of {an} is SN (I) find SN (II) finding the first n terms and TN of sequence {1 / Sn} I can do the first question,
(1) ∵ arithmetic sequence {an} satisfies A3 + A4 = 16, A4 + A5 = 20, ∵ 2A1 + 5q = 162a1 + 7q = 20 ∵ A1 = 3, q = 2 ∵ Sn = Na1 + n (n-1) d / 2 = n & # 178; + 2n (2) 1 / Sn = 1 / (n & # 178; + 2n) = 1 / N (n + 2) = 1 / 2 [1 / n-1 / (n + 2)] ∵ TN = 1 / S1 + 1 / S2 +... + 1 / Sn = 1 / 2 [1-1 / 3 + 1 / 2-1 / 4 + 1 / 3-1 / 5 +... + 1 / 1 / 3-1 / 5 +... + 1 / 1 /
RELATED INFORMATIONS
- 1. Given that the sum of the first n terms of two arithmetic sequences {an} and {BN} is an and BN respectively, and anbn = 7n + 45N + 3, then the number of positive integers n with anbn as an integer is () A. 2B. 3C. 4D. 5
- 2. If the sum of the first n terms of two arithmetic sequences {an} and {BN} is an and BN respectively, and an / BN = 7n + 45 / N + 3, then the number of positive integers n with an / BN as an integer is? First of all, thank you
- 3. Given that the sum of the first n terms of two arithmetic sequences {an} and {BN} is an and BN respectively, and anbn = 7n + 45N + 3, then the number of positive integers n with anbn as an integer is () A. 2B. 3C. 4D. 5
- 4. Given that the sum of the first n terms of two arithmetic sequences {an} and {BN} is an and BN respectively, and anbn = 7n + 45N + 3, then the number of positive integers n with anbn as an integer is () A. 2B. 3C. 4D. 5
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- 6. It is known that SM and Sn respectively represent the sum of the first m terms and the first n terms of the arithmetic sequence {an}, and smsn = m2n2, then aman=______ ．
- 7. In the equal ratio sequence {an}, the sum of the first n terms is SN. If SM, SM + 2, SM + 1 are equal difference sequence, then am, am + 2, am + 1 are equal difference sequence. (1) write the inverse proposition of this proposition; (2) judge whether the inverse proposition is true? The proof is given
- 8. It is known that the fine brushwork Q of equal ratio sequence is not equal to 1, and am, an and AP are equal ratio sequence. It is proved that m, N and P are equal difference sequence
- 9. The sequence {an} is an equal ratio sequence, m, N, P are equal difference sequence, if am = 4, an = 6, then the value of AP is equal
- 10. Three real numbers that are not equal to each other form an arithmetic sequence. If these three numbers are properly arranged, they can become an equal ratio sequence, and the sum of these three numbers is 6, then these three numbers can be calculated
- 11. The sum of the first n terms of the arithmetic sequence {an} is Sn, and a4-a2 = 8, A3 + A5 = 26. Note TN = snn2, if there is a positive integer m, so that TN ≤ m holds for all positive integers n, then the minimum value of M is______ ．
- 12. It is known that the positive term sequence {an}, {BN} satisfies the following conditions: for any positive integer n, an, BN, a (n + 1) are equal difference sequence, BN, a (n + 1), B (n + 1) are equal ratio sequence, And A1 = 10, A2 = 15 Verification: sequence (root BN) is arithmetic sequence General formula for solving sequence {an}, {BN} Let Sn = 1 / (A1) + 1 / (A2) + 1 / (A3) +. 1 / (an) for any positive integer n, the inequality 2asn
- 13. How to extend m + n = P + Q AP + AQ = am + an to three terms in arithmetic sequence
- 14. In the arithmetic sequence, if M + n = P, then am + an = AP? In the arithmetic sequence, if M-N = P, then am an = AP?
- 15. In the arithmetic sequence, if M + n = P, then am + an = AP holds?
- 16. If M + n = P + Q + R, am + an = AP + AQ + Ar holds?
- 17. If M + n = P + Q, M N P Q ∈ n *, there is am + an = AP + AQ in the arithmetic sequence, what about in the arithmetic sequence?
- 18. In the arithmetic sequence {an}, M-N = Q-P, then am an = AQ AP
- 19. It is known that {an} is an arithmetic sequence. When m + n = P + Q, is there necessarily am + an = AP + AQ?
- 20. It is known that the sequence {an} is an equal ratio sequence, m, N, P ∈ n *, and m, N, P is an equal difference sequence