Question

What is a possible value for the missing term of the geometric sequence 1250 ___ 50

Answer 1

The possible value for the missing term of the geometric sequence = 250

Step-by-step explanation:

The given  geometric sequence:

1250, _______ ,50

Let x be the possible the missing term.

To find, the possible value for the missing term of the geometric sequence = ?

1250, x , 50

Here, first term($a_{1}$) = 1250, second term($a_{2}$) = x and

third term($a_{3}$) = x

We know that,

∴ Common ratio (r) = $\dfrac{a_{2}}{a_{1}} =\dfrac{a_{3}}{a_{2}}$

$\dfrac{x}{1250} =\dfrac{50}{x}$

⇒ x × x = 50 × 1250

⇒ $x^{2}$ = 62500

⇒ x = $\sqrt{62500}$

⇒ x = 250

∴ The possible value for the missing term of the geometric sequence = 250