Question

A sequence is defined by the recursive function f(n + 1) = –10f(n). If f(1) = 1, what is f(3)? 3 –30 100 –1,000

Answer 1

Answer:

100

Step-by-step explanation:

Given:

f(1)=1

f(n+1) = - 10 f(n)

put n=1,

f(2) = -10 f(1)

f(2) = -10(1) = -10

put n=2,

f(3)= - 10 f(2)

f(3)= -10(-10)

f(3)= 100

Answer 2

it is given that a sequence is defined by the recursive, f(n + 1) = - 10f(n) and f(1) = 1

put n = 1 ,

f(1 + 1) = -10f(1)

or, f(2) = -10 × f(1) = -10 × 1 = -10

hence, f(2) = -10 ..........(1)

again, put n = 2

f(2 + 1) = -10f(2)

or, f(3) = -10f(3)

our equation (1),

f(3) = -10 × -10 = 100

hence, f(3) = 100