Question

What is a possible value for the missing term of the geometric sequence 37, __,333

Answer 1

Th given terms is,

`37,\ldots,333_{}`

Let 37 be the first term and 333 be the third term of a GP series.

`\begin{gathered} a_1=(a)/(r)=37 \\ a_2=a=x \\ a_3=ar=333 \end{gathered}`

Here, a is the second term x.

The product of the first and the third term is,

`\begin{gathered} a_1* a_3=(a)/(r)*(ar) \\ 37*333=a^2 \\ a^2=12321 \\ a=\sqrt[]{12321} \\ a=\pm111 \end{gathered}`

Thus, the possible values of the second term is 111 or -111.