How to prove that an is equal difference function and equal ratio function

A (n + 1) - an = constant, it can be proved that an is an isochromatic function;
A (n + 1) / an = constant, it can be proved that an is a proportional function;

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1. Why is the general term formula sn-sn-1 instead of Sn + 1-sn, and why is it segmented A1 = S1 and sn-sn-1
2. 1. Given 2 radical 3sin ^ 2 α + (2 radical 2-radical 3) sin α cos α - radical 2cos ^ 2 α = 0, α ∈ (π / 2, π), find sin2 α 2. Given the function f (x) = 4sinxsin ^ 2 (π / 4 + X / 2) + cos2x, let the constant ω > 0, if the minimum positive period of y = f (ω x) is π (1) Find the value of ω (2) find the maximum value of G (x) = f ^ 2 (ω x) + 2F (ω x) 3. The three internal angles a, B and C of △ ABC satisfy cos2b = CoSb (1) Find the size of angle B (2) find the value range of sina + sinc
3. Let f (x) = SiNx * (cosx radical 3sinx) (1) Find the monotone increasing interval of function f (x) on [0, π], (2) If the corresponding sides of the internal angles a, B, C of △ ABC are a, B, C respectively, and f (b) = 0, a, B, and the root 3C forms an arithmetic sequence with tolerance greater than 0, the value of sina / sinc can be obtained
4. The minimum value of the function y = arccosx + 10 arccosx is______ ．
5. 1: In △ ABC, let Tana / tanb = 2C-B / B, find the value of a? 2: in △ ABC, a + B = 10, COSC is a root of the square of equation 2x - 3x-2 = 0, find the minimum value of perimeter of △ ABC?
6. Evaluation: sin50 degrees (1 + root 3 times tan10 degrees) Please write down the process of simplification
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8. In △ ABC, let a + C = 2B, a-c = π 3, find the value of SINB
9. What is nonmonotonic in a certain interval
10. What is the implication number?
11. How to judge whether a general term formula is an arithmetic or proportional sequence
12. How to find the general term formula of the mixed sequence of equal difference and equal ratio?
13. Find out the triangle and circle. The number represented by the square? Triangle + square + circle = 40, triangle + circle + square + square = 46, triangle + circle
14. Triangle plus square is equal to 240, a triangle is equal to three square, ask triangle more than ten, square more than ten?
15. Triangle + square = 35, triangle + circle = 52, square + circle =?
16. 2 circle + triangle + box = 66 2 triangle + box + circle = 62 2 Box + circle + triangle = 64 circle = () triangle = () box = ()
17. Box = circle + triangle, triangle = 2 circle, if triangle = 4, then box = () How do you do it?
18. 1 triangle + square + circle = 23 kg, 2 square + 2 circle = 22 kg, 2 triangle + 1 circle = 28 kg. What is the weight of triangle, circle and square?
19. Circle plus triangle = 43 circle plus square = 37 triangle + square = 40 circle plus square
20. Circle plus positive equals 72, three plus positive equals 58, triangle plus circle equals 43, what is triangle equal to, circle equal to, positive equal to