Question

A sequence is defined by the recursive function f(n+1)=f(n)-2

If f(1)=10 what is f(3)?

Answer 1

Given :-

• A sequence is defined by f(n + 1) = f(n) -2 .
• f(1) = 10

To Find :-

• The value of f(3) .

Solution :-

As per Question ,

→ f(n + 1) = f(n) - 2

→ f(n + 1 ) - f(n ) = -2

Therefore , the second term of the sequence is ,

→ f(2) - f(1) = -2

→ f(2) - 10 = -2

→ f(2) = 10 -2

→ f(2) = 8

Similarly,

→ f(3) - f(2) = -2

→ f(3) = 8 -2

→ f(3) = 6

Hence the value of f(3) is 6 .

Answer 2

f(3) = 6

Explanation:

Using the recursive rule and f(1) = 10 , then

f(2) = f(1) - 2 = 10 - 2 = 8

f(3) = f(2) - 2 = 8 - 2 = 6