Question

Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.

–72, –71, –70, –69, ..

Answer 1

-73 +n

the first term is -73+1

the secound is -73+2

and so on

Answer 2

`a_(n)`= n - 73

Explanation:

there is a common difference between consecutive terms , that is

- 71 - (- 72) = - 70 - (- 71) = - 69 - (- 70) = 1

this indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 72 and d = 1 , then

`a_(n)` = - 72 + 1(n - 1) = - 72 + n - 1 = n - 73