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Home » The Fibonacci sequence is defined by a1 = 1 = a2, an = an–1 + an–2 for n > 2. Find (an+1)/an for n = 1, 2, 3, 4, 5.
The Fibonacci sequence is defined by a1 = 1 = a2, an = an–1 + an–2 for n > 2. Find (an+1)/an for n = 1, 2, 3, 4, 5.
Arithmetic Progressions | CBSE | Class 11 | Exercise 19.1 | Maths | RD Sharma
The Fibonacci sequence is defined by a1 = 1 = a2, an = an–1 + an–2 for n > 2. Find (an+1)/an for n = 1, 2, 3, 4, 5.

3Answer:

an = an–1 + an–2

If n = 1,

(an+1)/an = (a1+1)/a1

= a2/a1

= 1/1

= 1

a3 = a3–1 + a3–2

= a2 + a1

= 1 + 1

= 2

If n = 2,

(an+1)/an = (a2+1)/a2

= a3/a2

= 2/1

= 2

a4 = a4–1 + a4–2

= a3 + a2

= 2 + 1

= 3

If n = 3,

(an+1)/an = (a3+1)/a3

= a4/a3

= 3/2

a5 = a5–1 + a5–2

= a4 + a3

= 3 + 2

= 5

If n = 4,

(an+1)/an = (a4+1)/a4

= a5/a4

= 5/3

a6 = a6–1 + a6–2

= a5 + a4

= 5 + 3

= 8

If n = 5,

(an+1)/an = (a5+1)/a5

= a6/a5 = 8/5

 

∴ Value of (an+1)/an when n = 1, 2, 3, 4, 5 are 1, 2, 3/2, 5/3, 8/5

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