Mathematics
ranana
41

State whether each sequence is arithmetic or geometric then find the next 2 terms in the sequence 1,6,36,216

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(1) Answers
Rothenberg746

Since the value is being multiplied by 6 as it increases, that means that n is an exponent. [latex] n(0)=6^{n}= 6^{0} =1\\ n(1) = 6^{1} = 6\\ n(2) = 6^{2} = 36\\ n(3) = 6^{3} = 316 [/latex] Since the sequence does not progress linearly but does progress at a consistent rate, the sequence is geometric. You find the next 2 terms by plugging the value into [latex] 6^{n} [/latex]. [latex] n(4) = 6^{4} = 1296\\ n(5)=6^{5} = 6480 [/latex]

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