Question

Is 301 in the sequence below? -9, -5,-1,3,7,...

Answer 1

Answer:

no

Step-by-step explanation:

Establish the nth term formula

There is a common difference d between consecutive terms, that is

d = - 5 - (- 9) = - 1 - (- 5) = 3 - (- 1) = 7 - 3 = 4

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 = - 9 and d = 4 , then

$a_{n}$ = - 9 + 4(n - 1) = - 9 + 4n - 4 = 4n - 13

Equate 4n - 13 to 301

4n - 13 = 301 ( add 13 to both sides )

4n = 314 ( divide both sides by 4 )

n = 78.5

Since n is not an integer then 301 is not in the sequence