Question

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Answer 1

|| ☆.QUESTION.☆ ||

Let, A be a sequence defined by$\mathrm{\: A_{1}\: =\: 1\, \:A_{2}\: = \:1\:and \:( A_{n} = A_{n-1}\:+ \:A_{n-2 })}$for all n>2, then the value of $\mathrm{\:\frac{A_{4}}{A_3}}$ is ..?

|| ✪.ANSWER.✪ ||

Given Here:-

• $\mathrm{\:A_{1}\:=\:1}$....(1)
• $\mathrm{\:A_{2}\: = \:1}$...(2)
• $\mathrm{\:A_{n}\: = \:A_{n-1}\: + \:A_{n-2}}$......(3)

Find Here:-

• Value of$\mathrm{\:\frac{A_{4}}{A_{3}}}$

Explanation:-

[ Keep value of n = 1,2,3,4,... in equation (3) ]

Case(1):-

• When, n = 3,

↪$\mathrm{\:A_{3}\: = \:A_{3-1}\:+\:A_{3-2}}$

↪$\mathrm{\:A_{3}\:=\:A_{2}\:+\:A_{1}}$

[Keep value by equ. (1) and (2) ]

↪$\mathrm{\:A_{3}\:=\:1\:+\:1}$

↪$\mathrm{\:A_{3}\:=\:2}$....(4)

Case(2):-

• When ,n = 4,

↪$\mathrm{\:A_{4}\:=\:A_{4-1}\:+\:A_{4-2}}$

↪$\mathrm{\:A_{4}\:=\:A_{3}\:+\:A_{2}}$

[ Keep value by equ. (2) and (4) ]

↪$\mathrm{\:A_{4}\:=\:2\:+\:1}$

↪$\mathrm{\:A_{4}\:=\:3}$...(5)

Now, Calculate

↪$\mathrm{\:\frac{A_{4}}{A_{3}}}$

[keep value by equ. (4) and (5) ]

↪$\bold{\mathrm{\bf{\:\frac{3}{2}\:(ANS).}}}$

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