leecole048 leecole048
  • 24-05-2021
  • Mathematics
contestada

Find the sum of the first 32 terms of the arithmetic sequence 24, 20, 16,

Respuesta :

jimrgrant1 jimrgrant1
  • 24-05-2021

Answer:

[tex]S_{32}[/tex] = - 1216

Step-by-step explanation:

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 24 and d = a₂ - a₁ = 20 - 24 = - 4 , then

[tex]S_{32}[/tex] = [tex]\frac{32}{2}[/tex] [ (2 × 24) + (31 × - 4) ]

     = 16(48 - 124)

     = 16 × - 76

     = - 1216

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