Question

1. what is the 5th term of the geometric sequence described by ( a_{n} = 5(1.5)^{n - 1} )?

( a_{5} = 5.0625 )
( a_{5} = 25.3125 )
( a_{5} = 37.96875 )
( a_{5} = 7.59375 )

Explanation:

Step1: Substitute n=5 into formula

$a_5 = 5(1.5)^{5-1}$

Step2: Simplify exponent

$a_5 = 5(1.5)^4$

Step3: Calculate $(1.5)^4$

$(1.5)^4 = 1.5\times1.5\times1.5\times1.5 = 5.0625$

Step4: Multiply by 5

$a_5 = 5\times5.0625$

Answer:

$a_5 = 25.3125$ (matches the second option)