Question

Maxim and Salma were asked to find an explicit formula for the sequence 54,63,72,81,... Maxim said the formula is f(n)=54+9n Salma said the formula is f(n)=9+54nf(n)=9+54n. Which one of them is right?

Answer 1

ANSWER

The explicit rule is

$f(n) = 45+9n$

EXPLANATION

The given sequence is :

54,63,72,81,...

The first term of this sequence is

$a = 54$

The common difference is

$d =63 - 54 = 9$

The explicit rule is given by:

$f(n) = a + d(n - 1)$$f(n) = 54+9(n -1 )$

We expand to get:

$f(n) = 54+9n -9$

$f(n) = 45+9n$

None of them is correct .