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If a1 + A5 = 2, A3 + A7 = 6, then A5 + A9
eighteen
Obviously, the equivalent ratio is 1.732
The sequence {an} is an arithmetic sequence with non-zero tolerance, and A5, a8 and A13 are three adjacent terms of the arithmetic sequence {BN}. If B2 = 5, then BN = ()
A. 5•(53)n−1B. 5•(35)n−1C. 3•(35)n−1D. 3•(53)n−1
∵ {an} is an arithmetic sequence with non-zero tolerance, and A5, A8, A13 are the adjacent three terms of the arithmetic sequence {BN}, ∵ (A5 + 3D) 2 = A5 (A5 + 8D), ∵ A5 = 92d, ∵ q = A5 + 3da5 = 152d92d = 53, ∵ B2 = 5, q = 53, ∵ B1 = b2q = 3, ∵ BN = b1qn − 1 = 3 · (53) n − 1
The sequence {an} is an arithmetic sequence with non-zero tolerance, and A5, a8 and A13 are the adjacent three terms of the arithmetic sequence {BN}. (1) find the common ratio of the arithmetic sequence {BN}
an=a1+(n-1)d
a5=a1+4d
a8=a1+7d
a13=a1+12d
a5*a13=(a8)²
(a1+4d)*(a1+12d)=(a1+7d)²
d=2a1
a5=a1+4d=9a1
a8=a1+7d=15a1
a13=a1+12d=25
Common ratio q = 15:9 = 5 / 3
Let the first term A1 = 256 of the equal ratio sequence {an}, the sum of the first n terms be Sn, and Sn, Sn + 2, Sn + 1 form the equal difference sequence. (I) find the common ratio Q (2) of {an}, and use iin to express {an}
The product of the first n terms of
Iin = A1 * A2... An, try to compare the size of ii7, II8, ii9
For the known function f (x) = x + T / X (T > 0) and point P (1,0), two tangent lines PM and PN of the curve y = f (x) are made through point P, and the tangent points are m and N respectively
(1) Let / Mn / = g (T) try to find the expression of the function g (T);
(2) Whether there is t, so that m, N and a (1,0) are collinear. If there is, find out the value of T; if not, explain the reason
『3』 Under the condition of (1), if for any positive integer n, there are always m + 1 real numbers A1, A2,..., am, am + 1 in the interval [2, N + 64 / N], such that the inequality g (A1) + G (A2) +... + G (AM)
(n + 2) = Sn + s (n + 1 (n + 1 + 1) + a (n + 2)] = Sn + Sn + a (n + 1 (n + 1) + a (n + 1 + 1) + 2 (n + 2)] (Sn + n + 1 (n + 1) + a (n + 1 + 1) 2Sn + 2 (n + 1) 2Sn + 2 (n + 1) 2 (n + 1 + 1) + 2 [Sn + a (n + 1 + 1) + a (n + 1 (n + 1) + a (n + 2)] (Sn + 1 (n + 1 (n + 1) 2Sn + 1) 2Sn + 2Sn + 1 (n + 1) 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2Sn + 2 (n + 2 it's not easy
RELATED INFORMATIONS
- 1. A1 = 1, N, an, Sn are equal difference sequence. It is proved that {Sn + N + 2} is equal ratio sequence
- 2. 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
- 3. If q = - 1 / 2, then a1 + a3 + A5 / A3 + A5 + A7=
- 4. 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?
- 5. 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?
- 6. 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
- 7. 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
- 8. Proportional sequence, A3 and A9 are the two roots of equation x equal square + 3x + 1, A6=
- 9. If A3 = 3, A9 = 75, then a10=______ ．
- 10. In the equal ratio sequence {an}, A6 = 6, A9 + 9, then A3 is equal to?
- 11. In the equal ratio sequence {an}, a1 + A2 + a3 = - 3, A1 * A2 * A3 = 8,1, find an 2, find A1 * A3 * A5 * A7 * A9
- 12. In {an}, A3 = 1 / 2, A9 = 8, then the value of A5 * A6 * A7 is A9/A3=(A1×q^8)/(A1×q^2)=q^6=8/(1/2)=16 q^3=±4 How to get Q ^ 3 = ± 4 in this non analytic expression? That is, Q ^ 6 = 16, how to delimit Q ^ 3 = ± 4?
- 13. Equal ratio sequence a1 + A2 = 3, A3 + A4 = 6, find S8
- 14. In the arithmetic sequence an, the tolerance d = 1 / 2, A4 + A17 = 8, then A2 + A4 + A6 + +a20=?s20=?
- 15. If the tolerance of {an} is d = 1, A4 + A17 = 8, then A2 + A4 + A6 +... + A20 =? The online answer is like this a4+a17=8 So, 2a10 + D = 8 a10＝3．5 a11＝4．5 So, a2+a4+a6+...+a20 = 10 × a11 = 45
- 16. In the root sign 3-A divided by A-1, what is the value range of a?
- 17. Given (x + my) (x + NY) = x ^ 2-5xy + 3x ^ 2, find the algebraic formula 3mn-2 (M + n)
- 18. If 3x ^ A + 1y ^ B and - 1 / 2x ^ 3-ay ^ 2a are similar, then a = (), B = ()
- 19. This is about the addition and subtraction of integers There is such a problem: find the value of the polynomial y to the second power - 2XY + y + 1 / 2, where x = 10000 is mistaken for 1000, and the result is correct. Can you tell the Dao Li in it? You'll get points if you get it right!
- 20. An addition and subtraction problem of mathematical integral There is such a problem, "when a = 2, B = - 2", find the value of polynomial 2 (a ^ - 3AB + 3b) - 3 (- A ^ 2-2ab + 2b). Ma Xiaohu fried a = 2 into a = - 2. Wang Xiaozhen did not copy the wrong problem, but they all made the same result. Do you know what happened? Please explain the reason