edfrank2704 edfrank2704
  • 01-08-2018
  • Mathematics
contestada

Find the sum of the first seven terms of the sequence 4, 12, 36, 108, … .
a. 1,456B.1,457C.4,372D.4,374

Respuesta :

pinquancaro pinquancaro
  • 01-08-2018

The given sequence is 4,12,36,108....

Here we can observe the first term [tex] a_{1} [/tex] = 4 , [tex] a_{2}=12 [/tex] and so on.

The common ratio (r)=[tex] \frac{12}{4}=3 [/tex]

Since the common ratio is greater than 1,

Therefore the sum of the geometric series = [tex] \frac{a(r^{n}-1)}{r-1} [/tex]

Since we have to find the sum of first seven terms, so n=7

=[tex] \frac{4(3^{7}-1)}{3-1} [/tex]

=4372.

Therefore, option C is the correct answer.

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