mayc0lalu101 mayc0lalu101
  • 02-04-2020
  • Mathematics
contestada

Identify the 16th term of a geometric sequence where a1 = 4 and a8 = −8,748.

−172,186,884
−57,395,628
57,395,628
172,186,884

Respuesta :

sqdancefan
sqdancefan sqdancefan
  • 02-04-2020

Answer:

 −57,395,628

Step-by-step explanation:

The n-th term of a geometric sequence is given by ...

  an = a1·r^(n-1)

Then the ratio of the 8th term to the 1st term is ...

  a8/a1 = (a1·r^(8-1))/(a1·r^(1-1)) = r^7

and the common ratio is ...

  (-8748/4)^(1/7) = -3

That makes the 16th term be ...

  a16 = 4·(-3)^(16 -1) = -57,395,628

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