طلب مساعدة : متتابعة هندسية أوجد الحد 19

[Mathe]

احتاج الى مساعده في حل هذى السؤال:
:confused:
Question:
Consider the geometric sequence Yn , such that Y4 =10,Y6 =160

a) Write down the closed form of this sequence, and hence calculate the 19th term.





Yn
_____ b) Describe the long term behavior of the sequence
Yn-4





الواي و الان اس للربعه yn
c) If Xn =(-4) , find the first four terms of Xn. Is, Xn , a geometric sequence?



بليز ساعدوني

[uaemath]

Let the first term be a and the common ratio be r

Y₄ = ar³ = 10
Y₆ = ar⁵ = 160

\Large \frac {Y_{6}} {Y_{4}} = \frac{ar^5}{ar^3}= \frac{160}{10}

\Large \frac{r^5}{r^3}=r^2 = 16

\Large \ r=\pm 4

when r = 4 , ar³ = 10

a4³ = 10

a = 10/64

a = 5/32

The general term of a Geometric sequence is

Y_n = a r^n-1

http://www.uaemath.com/ar/aforum/math0636235001193280383.png


when r = - 4 , ar³ = 10

a (-4)³ = 10

a = -10/64

a = -5/32

The general term of a Geometric sequence is

Y_n = a r^n-1

http://www.uaemath.com/ar/aforum/math0839362001193280472.png

http://www.uaemath.com/ar/aforum/math0386236001193280880.png
⁴(4±) = Hence on the long term , it is constant

X_n = -4

This is a constant sequence

X₁ = X₂ = X₃= X₄= -4

Yes , it is a geometric sequence of first term = -4 and common ratio r = 1

[Mathe]

thanks

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