contestada

In a geometric sequence of real numbers, the sum of the first six terms is 9 times the sum of the first three terms. If the first term is 5, what is the third term?

Respuesta :

Answer:  The value of third term is 20.

Step-by-step explanation:

Since we have given that

Sum of the first six terms is 9 times the sum of the first three terms.

So, it becomes,

[tex]a+ar+ar^2+ar^3+ar^4+ar^5=9(a+ar+ar^2)\\\\x+r^3(a+ar+ar^2)=9x\\\\x+r^3x=9x\\\\x(1+r^3)=9x\\\\1+r^3=9\\\\r^3=9-1\\\\r^3=8\\\\r=2[/tex]

If a = 5

So, the value of third term would be

[tex]a_3=ar^2=5(2)^2=5\times 4=20[/tex]

Hence, the value of third term is 20.

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