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In {an}, A3 = 12, A5 = 48, then A7 = () A. 96B. 192C. 384D. 768
In ∵ equal ratio sequence {an}, A3 = 12, A5 = 48, ∵ a1q2 = 12a1q4 = 48, the solution is A1 = 3, Q2 = 4, ∵ A7 = a1q6 = 3 × 43 = 192
In the equal ratio sequence an, if A3 * A5 = 8, then A1 * A7=
Solution
An is equal
Then A3 × A5 = A1 × A7
∴a1×a7=8
In the equal ratio sequence {an}, if a3.a5 = 5, then the value of A1 * A7 is equal to
a1*a7
=a3/q^2*a5*q^2
=a3*a5
=5
It is known that the increasing sequence {an} satisfies A2 + a3 + A4 = 28, and A3 + 2 is the median of the difference between A2 and A4, if BN = log (2An + 1) (at the bottom right of log)
It is known that the increasing proportional sequence {an} satisfies A2 + a3 + A4 = 28, and A3 + 2 is the median of the differences of A2 and A4, if BN = log (2An + 1) (at the bottom right of log). SN is the sum of the first n terms of the sequence {anbn}, then SN is obtained
A2 + a3 + A4 = 28, A2 + A4 = 2 (A3 + 2) leads to A3 = 8, A2 + A4 = 20, A2 = a1q, A3 = a1q ^ 2, A4 = a1q ^ 3 leads to q = 2 or 1 / 2 increasing, then q = 2 Sn = log2 (A2) + log2 (A3) +.. + log2 (a (n + 1)) = log2 (a2a3.. a (n + 1)) = log2 (2 ^ n * 2 ^ (n (n + 1) / 2)) = (n ^ 2 + 5N + 2) / 2
RELATED INFORMATIONS
- 1. In the sequence {an}, A1 ＞ 0, a3-a2 = 8, and the middle term of A1, A5 is 16 (1) Let BN = log4an, the sum of the first n terms of the sequence {an} be Sn, whether there is a positive integer k such that 1 / S1 + 1 / S2 + 1 / S3 + +1 / Sn ＜ K holds for any n ∈ n * constant? If it exists, find the minimum value of positive integer K. if it does not exist, explain the reason
- 2. A 1 = 1, a 5 = 8A 2, B N = an + N, find the sum of the first n terms of B n
- 3. (2014. The three module in Hexi District) set Sn as the first n term and the 8a2+a5=0 of the geometric sequence {an}, then S5S2 equals (). A. 11B. 5C. -8D. -11
- 4. If a (n + 1) < an, A2 × A8 = 6, A4 + A6 = 5, then A5 / A7 is equal to______
- 5. If the sequence {an} is an equal ratio sequence composed of positive numbers and the common ratio is not 1, then the size relationship between a1 + A8 and A4 + A5 is () A. A1 + A8 ＞ A4 + a5b. A1 + A8 ＜ A4 + a5c. A1 + A8 = A4 + a5d
- 6. If A5 = 4 in {an}, then A2 · A8 is equal to
- 7. In the equal ratio sequence an, a1 + a3 = 4, A2 + A9 = 8, find S8
- 8. {an} is an equal ratio sequence. If A8 is equal to 2 than A4 and S4 = 4, then the value of S8 is equal to 4 Specific steps and methods should be taken
- 9. If A2 = 9, A5 = 243, then the sum of the first four terms of {an} is 120,
- 10. In the equal ratio sequence {an} with known common ratio 2, A2 + A5 + A8 + a11 + A14 + A17 + A20 = 13, then what is the sequence A1? (find the whole process)
- 11. If A3 = - 4, A6 = 4, then A9=
- 12. In the equal ratio sequence {an}, A6 = 6, A9 + 9, then A3 is equal to?
- 13. If A3 = 3, A9 = 75, then a10=______ ．
- 14. Proportional sequence, A3 and A9 are the two roots of equation x equal square + 3x + 1, A6=
- 15. The arithmetic sequence an is an increasing sequence, the sum of the first n terms is Sn, and A1, A3 and A9 are equal proportion sequence, S5 = the square of A5. The general term formula of the sequence an is obtained
- 16. Let positive number sequence {an} be equal ratio sequence, and A2 = 4, A4 = 16, find [LGA (n + 1) + LGA (n + 2) + +The value of the limit of LGA (2n)] / N ^ 2
- 17. In {an} where all items are positive proportional sequence, A2 * A4 = 4, a1 + A2 + a3 = 14, then the value of the largest positive integer n with an + an + 1 + an + 2 > 1 / 9 is satisfied?
- 18. It is known that SN is the sum of the first n terms of the equal ratio sequence {an}, S2, S6 and S4 are equal difference sequence, and the common ratio Q of the sequence {an} is obtained?
- 19. If q = - 1 / 2, then a1 + a3 + A5 / A3 + A5 + A7=
- 20. It is known that real number sequence an is equal ratio sequence, where A7 = 1, and A4, A5 + 1, A6 are equal difference sequence. The general term formula of sequence an is obtained fast