youness3083 youness3083
  • 21-05-2020
  • Mathematics
contestada

Write an explicit formula for a(n) the n^th term of the sequence 23, 31, 39, ...

Respuesta :

jimrgrant1 jimrgrant1
  • 21-05-2020

Answer:

[tex]a_{n}[/tex] = 8n + 15

Step-by-step explanation:

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

d = 39 - 31 = 31 - 23 = 8

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 = 23 and d = 8, thus

[tex]a_{n}[/tex] = 23 + 8(n - 1) = 23 + 8n - 8 = 8n + 15 ← explicit formula

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