Find out the wrong term from the given series | vedclass

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Question

(C) The given series is $1, 3, 7, 15, 27, 63, 127$.Let us analyze the differences between consecutive terms:$3 - 1 = 2 = 2^1$$7 - 3 = 4 = 2^2$$15 - 7

Vedclass · Accepted Answer

$27$

Vedclass · Answer

(C) The given series is $1, 3, 7, 15, 27, 63, 127$.Let us analyze the differences between consecutive terms:$3 - 1 = 2 = 2^1$$7 - 3 = 4 = 2^2$$15 - 7 = 8 = 2^3$$27 - 15 = 12$$63 - 27 = 36$$127 - 63 = 64 = 2^6$The pattern of differences should be powers of $2$ $(2^1, 2^2, 2^3, 2^4, 2^5, 2^6)$.Following this pattern,the difference after $15$ should be $2^4 = 16$.So,the next term should be $15 + 16 = 31$.Then,the next difference should be $2^5 = 32$,and $31 + 32 = 63$,which matches the next term.Therefore,$27$ is the wrong term in the series.

Find out the wrong term from the given series: $1, 3, 7, 15, 27, 63, 127$.

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