3, 6, 21, 28, 55, 66, ?, 120 | vedclass

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Question

(C) Let the given series be $3, 6, 21, 28, 55, 66, x, 120$.Observe the pattern by splitting the series into two alternating sub-series:Sub-series $1$

Vedclass · Accepted Answer

$105$

Vedclass · Answer

(C) Let the given series be $3, 6, 21, 28, 55, 66, x, 120$.Observe the pattern by splitting the series into two alternating sub-series:Sub-series $1$ (odd positions): $3, 21, 55, x$Differences: $21-3 = 18$,$55-21 = 34$,$x-55 = ?$Sub-series $2$ (even positions): $6, 28, 66, 120$Differences: $28-6 = 22$,$66-28 = 38$,$120-66 = 54$Analyzing the second sub-series differences: $22, 38, 54$. These are in an $A.P.$ with a common difference of $16$.Analyzing the first sub-series differences: $18, 34, ?$. These are also in an $A.P.$ with a common difference of $16$.Therefore,the next difference in the first sub-series is $34 + 16 = 50$.Thus,$x = 55 + 50 = 105$.

$3, 6, 21, 28, 55, 66, ?, 120$

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