emifrnco
emifrnco emifrnco
  • 01-07-2020
  • Mathematics
contestada

Write an
explicit formula for An, the nth term of the sequence 20, 30, 40, ....

Respuesta :

jimrgrant1 jimrgrant1
  • 01-07-2020

Answer:

[tex]A_{n}[/tex] = 10n + 10

Step-by-step explanation:

There is a common difference between consecutive terms in the sequence

d = 30 - 20 = 40 - 30 = 10

This indicates the sequence is arithmetic with explicit formula

[tex]A_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 20 and d = 10, thus

[tex]A_{n}[/tex] = 10 + 10(n - 1) = 10 + 10n - 10 = 10n + 10

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