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In the arithmetic sequence {an}, if A1, A3 and A4 form an arithmetic sequence, then the common ratio of the arithmetic sequence is______ ．
Let {an} tolerance be D, ∵ A1, A3, A4 be equal ratio sequence, ∵ A32 = a1a4, that is, (a1 + 2D) 2 = A1 (a1 + 3D), and the solution is d = 0 or A1 = - 4D. If d = 0, then the common ratio of equal ratio sequence is q = 1. If A1 = - 4D, then the common ratio of equal ratio sequence is q = a3a1 = − 2D − 4D = 12
The common ratio in the arithmetic sequence {an} is 3. If A1, A3 and A4 are in the arithmetic sequence, then A2 =?
The tolerance is 3
Then A3 = a1 + 2 * 3 = a1 + 6
a4=a1+3*3=a1+9
A1, A3, A4 are equal ratio sequence
Then (A3) ^ 2 = A1 * A4
(a1+6)^2=a1*(a1+9)
a1^2+12a1+36=a1^2+9a1
a1=-12
So A2 = a1 + 3 = - 12 + 3 = - 9
It is known that all items of the equal ratio sequence {an} are positive and A1, one-half A3 and A2 are equal difference sequence, then A3 + A4 of A4 + A5 is equal
If the common ratio is Q and the first term is A1, then A1, one-half A3 and A2 form an arithmetic sequence/
A3 = a1 + A2, that is, A1 * q ^ 2 = a1 + A1 * q
Q ^ 2 = 1 + Q, q = (1 + √ 5) / 2 can be obtained
(a3+a2)/(a4+a5)
=(a1*q^2+a1*q^3)/(a1*q^3+a1*q^4)
=(q+1)/(q^2+q)
=1/q
=2/(1+√5)
=(√5-1)/2
I wish you progress in your studies
It is known that an is an equal ratio sequence, A1 plus A2 equals half, A3 plus A4 equals 1, and A7 plus A8
When x is greater than 0, the maximum value of F (x) = 2x / x plus 1 is? How to solve this problem?
The {an} is an equal ratio sequence,
Then a1 + A2, A3 + A4, A5 + A6, a7 + A8 are also equal ratio sequences
Common ratio q = (A3 + A4) / (a1 + A2) = (1 / 2) / (1) = 1 / 2
a7+a8=(a1+a2)*(1/2)^3=1/8
RELATED INFORMATIONS
- 1. In {an}, an + 1 > an, a1 + A4 = 9, A2 * A3 = 8, S10 =?
- 2. In the known sequence (an), a1 + A2 = 9, a1a2a3 = 27, Sn =? I still can't find A1 and Q. how can I find them
- 3. It is known that SN is the sum of the first n terms of a sequence, and Sn = PN determines whether an is an equal ratio sequence
- 4. Let the first term A1 of the arithmetic sequence {an} be a, and the sum of the first n terms be SN. If s1s2s3 is a proportional sequence, find the general term formula of the sequence {an} …
- 5. The sum of the first n terms of sequence an is Sn A1 = 1 for any n > = 2 3sn-4 an 2-3s (n-1) / 2 General term formula for calculating the value of A2 A3 by assembly arithmetic sequence
- 6. It is known that {an} is an equal ratio sequence, and Sn is the sum of its first n terms. If A2 * A3 = 2A1, and the median of the difference between A4 and 2a7 is 5 / 4, then S5=
- 7. 1. In the arithmetic sequence {an}, if 2A1 = - A2 is known, then the common ratio is? 2. In the arithmetic sequence {an}, A1 = 3, A100 = 36, then A3 + A98 =? 3. In the sequence {an}, if an + 1-an = 1 / 2 (n = 1,2, ···), and A1 = 2, then A101 =? 4. In the arithmetic sequence {an}, a1 + A2 = 3, A3 + A4 = 6, then A7 + A8 =? 5. If the third and fourth terms of an equal ratio sequence {an} are 4 and 8 respectively, then the first and fifth terms are? 6. Given the sequence {an}, an = PN + Q (P, q are constants, you ∈ n *), where a1 = 2, A17 = 66, find (1) the general term formula an. (2) the first 10 terms and S10
- 8. Given the arithmetic sequence {an}, A1 = 1, an = a (n + 1) + 2 (n ≥ 1), then what is A100?
- 9. In the arithmetic sequence an, a1 + A2 +. + A50 = 200, A51 + a52 +... + A100 = 2700, then the value of A1 is?
- 10. In the arithmetic sequence {an}, a1 + A2 + +a50=200，a51+a52+… +If A100 = 2700, then A1 equals () A. -1221B. -21.5C. -20.5D. -20
- 11. In the equal ratio sequence {an}, TN is the product of the first n terms. If T5 = 1, then there must be () A. a1=1B. a3=1C. a4=1D. a5=1
- 12. In the sequence {an}, A1 = 3, an = 2A (n-1) + n-2 (n is equal to 2, and N belongs to n positive), it is proved that the sequence {an + n} is an equal ratio sequence In the sequence {an}, A1 = 3, an = 2A (n-1) + n-2 (n is greater than or equal to 2, and N belongs to n positive), it is proved that the sequence {an + n} is an equal ratio sequence, and the general term formula of {an} is obtained
- 13. The sum of the first n terms of the proportional sequence {an} is Sn if s2n = 3 (a1 + a3 +...) +A2n-1), a1a2a3 = 8, then A10 equals () A. -512B. 1024C. -1024D. 512
- 14. Given that the sum of the first n terms of the equal ratio sequence {an} is Sn = (2 ^ n) - 1, find the sum of the first n terms of the sequence {(an) ^ 2} and TN
- 15. In the arithmetic sequence {an}, a1 + a3 + A5 = 18, an-4 + An-2 + an = 108, Sn = 420, then n=______ ．
- 16. It is known that in the arithmetic sequence an, A4 = 4, the first 10 terms and S10 = 10, BN = (1 / C) are to the power of an, (C is a positive constant.) (1) Find an (2) It is proved that BN is an equal ratio sequence (3) Finding the first n terms and TN of sequence BN
- 17. Let f (x) satisfy 2F (x) - f (1 / x) = 4x-2 / x + 1, sequence {an} and {BN} satisfy A1 = 1, a (n + 1) - 2An = f (n), BN = a (n + 1) - an Finding the analytic expression of F (x) The general term formula of BN Is to compare the size of 2An and BN, and prove that
- 18. Given that the sum of the first n terms of sequence {an} A1 = 2 is Sn and satisfies Sn sn-1 = 3an, the general term formula an of sequence {an} is obtained Given that the sum of the first n terms of the sequence {an} A1 = 2 is Sn and satisfies Sn + sn-1 = 3an, the general term formula an of the sequence {an} is obtained
- 19. In the sequence an, A1 = in, a (n + 1) = 2An + 3n-4, in is a real number. For any in, it is proved that an is not an equal ratio sequence BN = a (n + 1) - an + 3, try to judge whether BN is an equal ratio sequence The formula of finding the same term of an
- 20. It is known that an = 2A (n-1) + 2 ^ n-1 (n ≥ 2) A1 = 5, A2 = 13, A3 = 33, A4 = 81. {(an + α) / 2 ^ n} is an arithmetic sequence, and a is obtained