Find the odd number in the given sequence: 1, | vedclass

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Question

(A) Let us analyze the pattern of the series: $1, 3, 7, 19, 42, 89, 184$.Step $1$: $1 	imes 2 + 1 = 3$Step $2$: $3 	imes 2 + 1 = 7$Step $3$: $7 	im

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(A) Let us analyze the pattern of the series: $1, 3, 7, 19, 42, 89, 184$.Step $1$: $1 	imes 2 + 1 = 3$Step $2$: $3 	imes 2 + 1 = 7$Step $3$: $7 	imes 2 + 5 = 19$This does not seem to follow a consistent rule.Let us try another pattern: $x_{n+1} = x_n 	imes 2 + k$,where $k$ increases by $1$ each time $(1, 2, 3, 4, 5, 6)$:$1 	imes 2 + 1 = 3$$3 	imes 2 + 2 = 8$ (Instead of $7$)$8 	imes 2 + 3 = 19$$19 	imes 2 + 4 = 42$$42 	imes 2 + 5 = 89$$89 	imes 2 + 6 = 184$Since $7$ is the term that breaks the pattern $x_n 	imes 2 + k$,it is the odd number in the sequence. Therefore,option $A$ is the correct answer.

Find the odd number in the given sequence: $1, 3, 7, 19, 42, 89, 184$.

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