Answer:
The formula is ⇒ [tex]\frac{-1}{2}(\frac{3}{5})^{n-1}[/tex]
Step-by-step explanation:
∵ The sequence is -1/2 , -3/10 , -9/50 , -27/250
∵ (-3/10) ÷ (-1/2) = 3/5
∵ (-9/50) ÷ (-3/10) = 3/5
∴ It is a geometric sequence
∴ The formula is Tn = ar^(n - 1)
Where a is the first term , r is the constant ratio between each two consecutive terms and n is the position of the number
∴ Tn = -1/2 ( 3/5)^(n - 1)
∴ [tex]Tn= \frac{-1}{2}(\frac{3}{5})^{n-1}[/tex]
