In the arithmetic sequence an with tolerance D and the arithmetic sequence BN with common ratio Q, A2 = B1 = 3, A5 = B2, A14 = B3

In the arithmetic sequence an with tolerance D and the arithmetic sequence BN with common ratio Q, A2 = B1 = 3, A5 = B2, A14 = B3

A1 + D = 3, ① a1 + 4D = 3q, ② a1 + 13D = 3q, ③ from ①, ②, ③ we get A1 = 1, d = 2, q = 3, so an = 2N-1, BN = 3 ^ n (the nth power of 3)
It is known that the sequence {an} is an arithmetic sequence with non-zero tolerance, and A1 = 1, and A2, A4 and A8 are equal proportion sequence. ① find the general term an; ② let BN = an2 ^ an find the sequence BN
Finding the first n terms of BN and Sn
1、an=a1+(n-1)d
a4²=a2*a8
(1+3d)²=(1+d)(1+7d)
1+6d+9d²=1+8d+7d²
d≠0
∴d=1
an=n
2、 bn=n2^n
Sn=1*2+2*2²+3*2³+…… +n2^n
2Sn= 1*2²+2*2³+…… +(n-1)2^n+n2^(n+1)
2Sn-Sn=1*2²+2*2³+…… +(n-1)2^n+n2^(n+1) - （1*2+2*2²+3*2³+…… +n2^n ）
Sn= -2-2²-2³-…… -2^n+n2^(n+1)
=n2^(n+1)-(2+2²+2³+…… +2^n)
Equal ratio sequence 2 + 2 & # 178; + 2 & # 179; + +2^n=2(1-2^n)/1-2=2(2^n-1)
∴Sn=n2^(n+1)-2(2^n-1)=(n-1)2^(n+1)+2
a4²=a2*a8
(a1+3d)²=(a1+d)(a1+7d)
a1²+6a1d+9d²=a1²+8a1d+7d² a1=1 d≠0
∴d=1
The general term an = 1 + (n-1) = n
bn=n2^n
As shown in the figure, take the three sides of RT △ ABC as the sides and make three squares outward. The area is expressed by S1, S2 and S3 respectively. It is easy to get some relations between S1, S2 and S3______ .
In RT △ ABC, AB2 = BC2 + ac2, ∵ S1 = AB2, S2 = BC2, S3 = ac2, ∵ S1 = S2 + S3
If point P moves on the curve y = x ^ 3-3x + (3-radical 3) + 3 / 4, and the inclination angle of the tangent passing through point P is a, then the value range of angle a is
[0, Wu) ∪ [(2 Wu) / 3, Wu]
Three equilateral triangles with three sides of RT △ ABC are made outwards, and their areas are expressed by S1, S2 and S3 respectively, so as to determine the relationship among S1, S2 and S3
S1 is the largest, S2 is the second, S3 is the smallest
(I haven't learned how to calculate the area of equilateral triangle yet)
Let RT △ ABC have three side lengths a, B and C respectively, where a is a hypotenuse and satisfies a & # 178; = B & # 178; + C & # 178;; the side lengths of three equilateral triangles are a, B and C. Because only one parameter (such as side length) is needed to determine an equilateral triangle, the area of the equilateral triangle is only related to the square of the side length