Question

which function defines the sequence 7,4,1,-2,-5... where f(8)=-14

Answer 1

A sequence can be arithmetic or geometric sequence

The function that defines the sequence is f(n) = 10 -3n

How to determine the function

The sequence is given as:

7,4,1,-2,-5...

The above sequence is an arithmetic sequence, with an initial value of 7, and a common difference of -3.

So, the function is:

$a_n = a +(n -1)d$

This gives

$a_n = 7 +(n -1)(-3)$

$a_n = 7 +3 -3n$

$a_n = 10 -3n$

Hence, the function that defines the sequence is f(n) = 10 -3n

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