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([tex]a_{1}[/tex]) = 1250, second term([tex]a_{2}[/tex]) = x and
third term([tex]a_{3}[/tex]) = x
We know that,
∴ Common ratio (r) = [tex]\dfrac{a_{2}}{a_{1}} =\dfrac{a_{3}}{a_{2}}[/tex]
[tex]\dfrac{x}{1250} =\dfrac{50}{x}[/tex]
⇒ x × x = 50 × 1250
⇒ [tex]x^{2}[/tex] = 62500
⇒ x = [tex]\sqrt{62500}[/tex]
⇒ x = 250
∴ The possible value for the missing term of the geometric sequence = 250
