Question

The first three terms of a Fibonacci sequence are: n 3n 4n What is the sixth term of the sequence?

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{The first three terms of a fibonacci sequence are n,2n,3n}$

$\underline{\textbf{To find:}}$

$\textsf{Sixth term of the sequence}$

$\underline{\textbf{Solution:}}$

$\underline{\textsf{Concept used:}}$

$\textsf{The n th term of the Fibonacci sequence is}$

$\mathsf{t_n=t_{n-2}+t_{n-1}\;\;where;n>2}$

$\mathsf{Here,}$

$\mathsf{t_1=n,\;t_2=2n,\;t_3=3n}$

$\mathsf{t_4=t_2+t_3}$

$\mathsf{t_4=2n+3n}$

$\implies\boxed{\mathsf{t_4=5n}}$

$\mathsf{t_5=t_3+t_4}$

$\mathsf{t_5=3n+5n}$

$\implies\boxed{\mathsf{t_5=8n}}$

$\mathsf{t_6=t_4+t_5}$

$\mathsf{t_6=5n+8n}$

$\implies\boxed{\mathsf{t_6=13\,n}}$