Question

The numbers $a_{1}, a_{2}, a_{3}, \ldots . .$ form an arithmetic sequence with $a_{1} \neq a_{2}$. The threenumbers $a_{1}, a_{2}$ and $a_{6}$ form a geometric sequence in that order. Then the commondifference of the arithmetic sequence is

• A. $a_{1}$
• B. $2 a_{1}$
• C. $3 a_{1}$
• D. $4 a_{1}$
• E. $5 a_{1}$

Answer 1

Answer: (C)

$a_{z}^{2}=a_{1} a_{6}=a_{1}\left(a_{a}+5 d\right)$
$\left(a_{1}+d\right)^{2}=a_{1}^{2}+5 a_{1} d$
$2 a_{1} d+d^{2}=5 a_{1} d$
$3 a_{1} d-d^{2}=0$
$d\left[3 a_{1}-d\right]=0$
$a \neq 0 \Rightarrow d=3 a_{1}$