In the arithmetic sequence {an} with known tolerance not 0, A1 = 2, some items of {an} form the arithmetic sequence {AKN} from small to large in the original order, and K1 = 1, K2 = 3, K3 = 11. (1) find the common ratio Q of the arithmetic sequence; (2) find AKN and kn

In the arithmetic sequence {an} with known tolerance not 0, A1 = 2, some items of {an} form the arithmetic sequence {AKN} from small to large in the original order, and K1 = 1, K2 = 3, K3 = 11. (1) find the common ratio Q of the arithmetic sequence; (2) find AKN and kn

(1) The ∵ sequence {an} is an arithmetic sequence, the first term A1 = 2, the tolerance D ≠ 0, some terms of {an} form the equal ratio sequence {AKN} from small to large in the original order, and K1 = 1, K2 = 3, K3 = 11. ∵ A1 · a11 = A23, that is, (2 + 2D) 2 = 2 · (2 + 10d), the solution is d = 3, that is, an = 2 + 3 (n-1) = 3n-1, ∵ q = a3a1 = 3 × 3 − 12 = 4. (2) from (1), AKN = 3kn-1 = 2 × 4N-1 = 22n-1, ∵ kn = 22n − 1 + 13

It is known that, as shown in the figure, the first-order function y = (K1-1) x + m intersects with the inverse scale function y = K2 / X at points a (2,4) and B (- 4, n)
(1) Find the value of K1, K2, m, n (2) find s △ AOB

(1)k2=xy=8
n=8/(-4)=-2
-2=-4(k1-1)+m
4=2(k1-1)+m
The solution is K1 = 2, M = 2
(2) Straight line y = x + 2, hyperbola y = 8 / X
Solution 1: let AB and Y axis intersect at C, then C (0,2)
S△AOB=S△AOC+S△BOC
The distance from a to y axis is 2, and the distance from B to y axis is 4
S△OAC=1/2*2*2=2,S△OBC=1/2*4*2=4
∴S△AOB=6
Solution 2: | ab | = √ [(4 + 2) & # 178; + (2 + 4) & # 178;] = 6 √ 2
The distance from O to AB is | 0 + 0 + 2 | / √ (1 + 1) = √ 2
S△AOB=1/2*√2*6√2=6

If x = 1 / 3, the inverse function y = K1 / X (K1 ≠ 0) is equal to the positive function y = k2x (K2 ≠ 0), then K1: K2 is equal to?

Make an equation: K1 / (1 / 3) = (1 / 3) K2
k1:k2=1:9