Question

In the four numbers first three are in G.P. and last three are in A.P. whose common difference is 6. If the first and last numbers are same, then first will be

Answer 1

We have,

Let the four number are $a+d,a-d,a,a+d$

Given that common difference is $6$, $d=6$

According to given question,

The first number is same the fourth number.

Now,

The first number are $a+d,a-d,a$ in G.P.

We know that,

${(a-6)}^2=a(a+6)$

$\Rightarrow a^2-12a+36=a^2+6a$

$\Rightarrow 18a=36$

$\Rightarrow a=2$

Hence, the first term is $a=2$

Hence, this is the answer.