Question

which term of the sequence 6,2,2/3,_____________ is 2/243

Answer 1

given series of gp because the ratio of sequence is same 6,2,2/3,_______is 2/243

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Answer 2

Step-by-step explanation:

given series is of G.P

because the ratio is same,

your series is,

6,2,2/3,--------------------

$r1 = \frac{6}{2} = 3 \\ \\ r2 = \frac{2}{ \frac{2}{3} } = 3$

hence ratio is same so it is a GP

then,by

$an = a {r}^{n - 1}$

on putting the value

$\frac{2}{243 } = 6 \times {3}^{n - 1} \\ \frac{1}{243 } = 3 \times {3}^{n - 1} \\ \frac{1}{243} = {3}^{n} \\ \frac{1}{ {3}^{5} } = {3}^{n} \\ {3}^{ - 5} = {3}^{n} \\ n = - 5$

proof:-

$an = 6 \times {3}^{ - 5 - 1} \\ \: \: \: \: \: \: \: = 6 \times {3}^{ - 6} \\ \: \: \: \: \: \: \: = 6 \times \frac{1}{ {3}^{6} } \\ \: \: \: \: \: \: \: = \frac{2}{243}$