Q14 of 74 Page 9

The Fibonacci sequence is defined by a1 = 1 = a2 , an = an-1 + an-2 (n > 2).
Find an+1/an, for n = 1, 2, 3, 4, 5.


Substituting n = 3, 4, 5 and 6 in an = an-1 + an-2
a3 = a3-1 + a3-2 = a2 + a1 = 1 + 1 = 2
a4 = a4-1 + a4-2 = a3 + a2 = 2 + 1 = 3
a5 = a5-1 + a5-2 = a4 + a3 = 3 + 2 = 5
a6 = a6-1 + a6-2 = a5 + a4 = 5 + 3 = 8
Substituting n = 1

Substituting n = 2, 3, 4 and 5 we get




The required series is 1, 2, 3/2, 5/3 and 8/5.

More from this chapter

All 74 →
12
Write the first five terms of each of the sequence in obtain the corresponding series a1 = -1, an = an-1/n, (n ≥ 2)

13
Write the first five terms of each of the sequence in obtain the corresponding series a1 = a2 = 2, an = an-1 – 1, (n > 2)

15
Find the sum of odd integers from 1 to 2001.

16
Find the sum of all natural numbers between 100 and 1000 which are multiples of 5.