What is the tenth term of this function?
f(1) = 30, f(n) = 3 × f(n − 1) − 90
+26397 What is the tenth term of this function?
f(1) = 30, f(n) = 3 × f(n − 1) − 90
fn=3fn−1−90f1=30f10= ?
f1=30f2=31f1−30⋅90f3=3f2−90=3(3f1−90)−90=32f1−31⋅90−30⋅90f4=3f3−90=3(32f1−3⋅90−90)−90=33f1−32⋅90−31⋅90−30⋅90f5=3f4−90=3(33f1−32⋅90−31⋅90−30⋅90)−90=34f1−33⋅90−32⋅90−31⋅90−30⋅90⋯fn=3n−1f1−3n−2⋅90−3n−3⋅90−…−30⋅90fn=3n−1f1−90⋅(3n−2+3n−3+…+1)⏟=3n−1−12fn=3n−1f1−90⋅3n−1−12fn=3n−1f1−45⋅(3n−1−1)⋯fn=−15⋅(3n−1−3)
fn=−15⋅(3n−1−3)f10=−15⋅(39−3)f10=−15⋅(19683−3)f10=−15⋅19680f10=−295200
