Find the missing number in the series: 3, 10, | vedclass

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Question

(A) Let the given series be $3, 10, 21, x, 51$.Calculate the differences between consecutive terms:$10 - 3 = 7$$21 - 10 = 11$$x - 21 = ?$$51 - x = ?$O

Vedclass · Accepted Answer

$34$

Vedclass · Answer

(A) Let the given series be $3, 10, 21, x, 51$.Calculate the differences between consecutive terms:$10 - 3 = 7$$21 - 10 = 11$$x - 21 = ?$$51 - x = ?$Observing the pattern of differences: $7, 11, ...$If we look at the differences of the differences,we see a pattern of adding prime numbers or alternating increments. However,checking the sequence $3, 10, 21, 36, 55$ (not matching) vs $3, 10, 21, 36, 55$ is not it.Let's re-examine: $3, 10, 21, 36, 55$ is not correct.Correct pattern: $3 + 7 = 10$,$10 + 11 = 21$,$21 + 15 = 36$,$36 + 19 = 55$ (if the last term was $55$).Given the sequence $3, 10, 21, ?, 51$:$3 + 7 = 10$$10 + 11 = 21$$21 + 15 = 36$$36 + 15 = 51$ (This does not fit).Let's try: $3 	imes 2 + 4 = 10$,$10 	imes 2 + 1 = 21$,$21 	imes 2 - 6 = 36$.Actually,the differences are $7, 11, 15, 19$ (adding $4$ each time).$3 + 7 = 10$$10 + 11 = 21$$21 + 15 = 36$$36 + 15 = 51$ is wrong. Let's check $36 + 15 = 51$ is $36 + 15 = 51$. Yes,$21 + 15 = 36$ and $36 + 15 = 51$. Wait,$36 + 15 = 51$. So the missing number is $36$. Since $36$ is not an option,let's re-evaluate.Maybe the differences are $7, 11, 13, 17$ (Prime numbers starting from $7$): $21 + 13 = 34$,$34 + 17 = 51$. This fits perfectly.Thus,the missing number is $34$.

Find the missing number in the series: $3, 10, 21, ?, 51$.

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