Mathematics

Find the next two terms of the series :
2 - 6 + 18 - 54 ………….

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Since,

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

Hence, the above series is a G.P. with r = -3 and a = 2.

We know that n^th term of G.P.,

a_n = ar^{n - 1}

Next two terms of the series are 5^th and 6^th.

⇒ a₅ = ar⁴

= 2.(-3)⁴

= 2 × 81

= 162.

⇒ a₆ = ar⁵

= 2.(-3)⁵

= 2 × -243

= -486.

Hence, the next two terms are 162 and -486.

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