A multiple choice question related to sequence If we know that a, B and C are in equal proportion sequence, M is the median of a and B, and N is the median of B and C, then (A / M) + (C / N) is equal to A.1 B.2 C.1/2 D.1/4 Please give me a detailed derivation process or solution, or you can chat with me alone. If the idea is clear and easy to understand, I will add scores,

A multiple choice question related to sequence If we know that a, B and C are in equal proportion sequence, M is the median of a and B, and N is the median of B and C, then (A / M) + (C / N) is equal to A.1 B.2 C.1/2 D.1/4 Please give me a detailed derivation process or solution, or you can chat with me alone. If the idea is clear and easy to understand, I will add scores,

Because a, B and C are in equal proportion sequence, AC = B ^ 2
And because m is the median of a and B, and N is the median of B and C, so
M = (a + b) / 2, n = (B + C) / 2, so
a/m + c/n
=2A / (a + b) + 2C / (B + C) (general)
=[2a(b+c)+2c(a+b)]/[(a+b)(b+c)]
=(2Ab + 2BC + 4ac) / (AB + BC + AC + B ^ 2) (from AC = B ^ 2)
=(2ab+2bc+4b^2)/(ab+bc+2b^2)
=2
That is, a / M + C / N = 2, B

A multiple choice question about sequence of numbers
The arithmetic sequence {an} with tolerance not equal to zero is related to the arithmetic sequence {BN}; A1 = B1, A3 = B3, a7 = B5, then:
A.b11=a13 B,b11=a31
C.b11=a63 D.b63=a11

The problem can be seen as a sequence of equal proportion of A1, A3 and A7, A3 * A3 = A1 * A7, (a1 + 2D) (a1 + 2D) = A1 (a1 + 6D) and the solution is A1 = 2D so A3 = 4D, a7 = 8D, so the common ratio of {BN} is the root 2 (root 4D / 2D), and then one generation after another ~! The answer is C (all 64D)

If A1 = 1, then S4 = ()
A. 7B. 8C. 15D. 16

∵ 4A1, 2A2, A3 are arithmetic sequences ∵ 4A1 + A32 = & nbsp; 2A2, ∵ 4A1 + A1 · q22 = 2a1q, that is, 4 + q22 = 2 & nbsp; Q ∵ q = 2 ∵ S4 = A1 (1 − Q4) 1 − q = 1 × (1 − 24) 1 − 2 = 15, so select C