anulikauwandu3
anulikauwandu3 anulikauwandu3
  • 20-09-2022
  • Mathematics
contestada

a G.P has 6 terms .if the 3rd term and the 4th terms are 28 and -56 respectively.find the common ratio,the first term ,and the sum of the G.P​

Respuesta :

caylus
caylus caylus
  • 20-09-2022

Answer:

Hello,

Step-by-step explanation:

[tex]u_2=u_1*r\\u_3=u_1*r^2\\u_4=u_1*r^3\\\\\dfrac{u_4}{u_3} =r=\dfrac{-56}{28} =\boxed{-2}\\\\u_1=\dfrac{u_3}{r^2} =\dfrac{28}{(-2)^2} =\dfrac{28}{4}=\boxed {7}\\\\\\\displaystyle\ s=\sum_{i=1}^6\ u_i\\\\=u_1*\sum_{i=1}^6\ r^{i-1}\\\\=7*\dfrac{(-2)^6-1}{-2-1} \\\\=-7*\dfrac{65}{3} \\\\\\\boxed{s=-\dfrac{455}{3} }\\[/tex]

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