1 = a_{1} = a_{2}

a_{n} = a_{n – 1 }+ a_{n – 2}, n > 2

So,

a_{3} = a_{2} + a_{1} = 1 + 1 = 2

a_{4} = a_{3} + a_{2} = 2 + 1 = 3

a_{5} = a_{4} + a_{3} = 3 + 2 = 5

a_{6} = a_{5} + a_{4} = 5 + 3 = 8

Substitute the values of 1 a and 2 a in the expression \( \dfrac{a_n+1}{a_n}\) for n=1

for n = 1, \( \dfrac{a_{1+1}}{a_1}= \dfrac{1}{1}=1\)

For n= 2, \( \dfrac{a_{2+1}}{a_2}= \dfrac{2}{1}=2\)

For n= 3, \( \dfrac{a_{3+1}}{a_3}= \dfrac{3}{2}\)

For n= 4, \( \dfrac{a_{4+1}}{a_4}= \dfrac{5}{3}\)

For n= 5, \( \dfrac{a_{5+1}}{a_5}= \dfrac{8}{5}\)

Answered by Pragya Singh | 2 years agoConstruct a quadratic in x such that A.M. of its roots is A and G.M. is G.

Find the geometric means of the following pairs of numbers:

**(i) **2 and 8

**(ii) **a^{3}b and ab^{3}

**(iii) **–8 and –2

Insert 5 geometric means between \( \dfrac{32}{9}\) and \( \dfrac{81}{2}\).