Question

F(1)=2 and f(n) = f(n-1) - 5; n-1

which of the following lists the terms in the sequence defined by this recursive function

a-2,3,8,13,18......
b-2,7,12,17,22.....
c-2,-3,-8,-13,-18.....
d-2,-7,-12,-17,-22....

Answer 1

Option c is correct.

The sequence is, 2, -3 , -8 , -13, -18, .....

Explanation:

Given the following as;

f(1) = 2

The recursive function is;
`f(n) = f(n-1) -5` ......[1]

to find the sequence defined by the recursive function;

Put n=2 in [1];

`f(2) = f(2-1) -5`

`f(2) = f(1) -5`

Substitute the value of f(1) = 2 we have;

`f(2) = 2-5 = -3`

Similarly, put n =3

`f(3) = f(3-1) -5`

`f(3) = f(2) -5`

Substitute the value of f(2) = -3 we have;

`f(3) = -3-5 = -8`

for n = 4 we have;

`f(4) = f(4-1) -5`

`f(4) = f(3) -5`

Substitute the value of f(3) = -8 we have;

`f(4) = -8-5 = -13` and so on .......

Therefore, we get the sequence defined by the recursive formula is,

2, -3 , -8 , -13, -18, .........