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What is the explicit formula for the sequence?

−1, 0, 1, 2, 3, . . .


an = n + 2


an = n − 2


an = an−1 − 2, where a1 = 3


an = an−1 − 2, where a1 = −1

Respuesta :

Answer:

[tex]a_{n}[/tex] = n - 2

Step-by-step explanation:

Note the difference between consecutive terms is constant, that is

0 - (- 1) = 0 + 1 = 1

1 - 0 = 1

2 - 1 = 1

3 - 2 = 1

This indicates the sequence is arithmetic with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 1 and d = 1, thus

[tex]a_{n}[/tex] = - 1 + n - 1 = n - 2

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