Question

Write an equation for the nth term of the geometric sequence 3584, 896, 224... Find the sixth term of this sequence

Answer 1

Explanation:

r =
`(a_n)/(a_(n-1)) = (896)/(3584) =  (1)/(4)`

Using the geometric series formula for the nth term:

`S_n = a \cdot (1-r^n)/(1-r) => S_(6) = 3584 \cdot (1 - ((1)/(4))^(6) )/(1 - (1)/(4) )  = 4777(1)/(2)`