Find the next number in the series: 5, 21, 69 | vedclass

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Question

(B) Analyze the differences between consecutive terms in the series: $5, 21, 69, 213, 645$.$21 - 5 = 16$$69 - 21 = 48$$213 - 69 = 144$$645 - 213 = 432

Vedclass · Accepted Answer

$1941$

Vedclass · Answer

(B) Analyze the differences between consecutive terms in the series: $5, 21, 69, 213, 645$.$21 - 5 = 16$$69 - 21 = 48$$213 - 69 = 144$$645 - 213 = 432$Observe the pattern in the differences: $16, 48, 144, 432$.Each difference is $3$ times the previous difference:$16 	imes 3 = 48$$48 	imes 3 = 144$$144 	imes 3 = 432$The next difference should be $432 	imes 3 = 1296$.Therefore, the next term in the series is $645 + 1296 = 1941$.

Find the next number in the series: $5, 21, 69, 213, 645, \dots ?$

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