Mathematics

Show that the progression 2, 6, 18, 54, 162,….. is a G.P.
Write its:
(i) first term
(ii) common ratio
(iii) nth term
(iv) 8th term.

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2, 6, 18, 54, 162,…..

$\Rightarrow \dfrac{18}{6} = \dfrac{6}{2}$ = 3.

Since, ratio between consecutive terms are equal, thus the series is in G.P.

a = 2

r = $\dfrac{6}{2}$ = 3

We know that,

nth term of a G.P. is given by,

⇒ T_n = ar^{n - 1}

= 2.(3)^{n - 1}.

⇒ T₈ = (2)(3)^{8 - 1}

= 2(3)⁷

= 2(2187)

= 4374.

Hence, a = 2, r = 3, T_n = 2.(3)^{n - 1}, T₈ = 4374.

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