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.
