Question

Find the next two numbers in the pattern 1,(-3),9,(-27),81,_,_.

Answer 1

$Given \: series : 1, (-3), 9, (-27), 81 , \red{?}$

/* By observing the series,we can find the following pattern */

$t_{n} = (-3)^{n-1} , \:Where \: n \in N$

$t_{1} = (-3)^{1-1} = (-3)^{0}= 1$

$t_{2} = (-3)^{2-1} =(-3)$

$t_{3} = (-3)^{3-1} = (-3)^{2} = 9$

$t_{4} = (-3)^{4-1} = (-3)^{3} = -27$

$t_{5} = (-3)^{5-1} = (-3)^{4} = 81$

$\red{ t_{6}} = (-3)^{6-1} = (-3)^{5} \green {= -243}$

Therefore.,

$\red { Next \: number \:in \:the \: pattern } \green {= -243 }$

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