f(1)=72 f(n)=f(n−1)+9 find an explicit formula for f(n)

= 9n + 63

generate the first few terms using the recursive equation

f(1) = 72

f(2) = 72 + 9 = 81

f(3) = 81 + 9 = 90

f(4) = 90 + 9 = 99

the sequence is 72, 81, 90, 99, .....

This is an arithmetic sequence whose n th term formula is

= + (n - 1 )d

where is the first term and d the common difference

d = 99 - 90 = 90 - 81 = 81 - 72 = 9 and = 72

= 72 + 9(n - 1) = 72 + 9n - 9 = 9n + 63 ← explicit formula

9n + 63

Step-by-step explanation:

90

step-by-step explanation:

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2