Question

If each term of a GP is positive and each term is the sum of its two succeeding terms, then the common ratio of the GP is

• A. $\frac{\sqrt{5}-1}{2}$
• B. $\frac{\sqrt{5}+1}{2}$
• C. $-\frac{\sqrt{5}+1}{2}$
• D. None of these

Answer 1

The correct option is A $\frac{\sqrt{5}-1}{2}$

in GP $a_n=a_1\times r^n$

given $a_{n+2}=a_{n+1}+a_n$

$⟹r^2=r+1$

$r^2-r-1=0$

$r=\frac{\sqrt{5}-1}{2}$ ($\because$r is positive)