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when n=1,tn=(-1)^1.2019= -2019
when n=2, tn=(-1)^2.2019= 2019
common ratio:-
t2/t1=2019/-2019=-1
i hope it is helpful for u
AnswEr :
The nth term of the GP is :
[tex] \sf \: T_n = ( - 1) {}^{n} \times 2019[/tex]
We have to find the common ratio
Putting n = 1,we would get the first term :
[tex] \sf \: T_1 = ( - 1) {}^{1} \times 2019 = - 2019[/tex]
Putting n = 2,we would get the second term :
[tex] \sf \: T_2 = {( - 1)}^{2}(2019) = 2019[/tex]
Now,
If r is the common ratio of the above GP
[tex] \implies \: \sf \: r = \dfrac{T_2}{T_1} \\ \\ \sf \implies r = \cancel{ - \dfrac{2019}{2019} } \\ \\ \implies \: \boxed{ \boxed { \sf \: r = - 1}}[/tex]