Question

The fith term of a G.P is 8 times the 2nd term find its common ratio​

Answer 1

Answer:

Common ratio r = 2

Step-by-step explanation:

$\because$ the fith term of a G.P is 8 times the 2nd term.

$\therefore \: t_5 = 8\times t_2 \\ \therefore \: ar^{5-1}=8\times \: ar^{2-1} \\ \therefore \: r^{4}=8\times \: r^{1} \\ \therefore \: r^{3}=8 \\ \therefore \:r^{3}= {2}^{3} \\ \hspace{20 pt}\huge \red{ \boxed{\therefore \:r= {2}}}$

Hence, common ratio is 2.

Answer 2

Answer:

The common ratio is 2

Step-by-step explanation:

T_n = ar^(n-1)

T_5 = 8(T_2)

r = ?

T_5 = ar^4

T_2 = ar

Therefore

ar^4 = 8ar

Divide both sides by ar, we have

r³ = 8

Taking the cube root of both sides, the result is

r = 2

The common ratio is 2