A sequence is given by 21/2,7,14/3... If the nth term is 56/27. Find n

Question

Find n. 

Answer 1

This is a geometric progression with q=2/3 [=7/(21/2)=(14/3)/7]

a_n=56/27

a_n=a₁*q^n-1

a₁=21/2

a₂=7  [=(a1*q)=(21/2)*(2/3)]

a₃=14/3  [=a2*q]

a₄=(14/3)(2/3)=28/9

a₅=(a₄)*q=(28/9)(2/3)=56/27

So n=5.

 Or you can find n from

56/27=(21/2)(2/3)^n-1

7*2³/3³=7(2/3)^n-2

(2/3)³=(2/3)^n-2

3=n-2

n=5