Find the missing number in the series: 7, 8, | vedclass

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Question

(A) The given series is $7, 8, 24, 105, 361, ?$.Let's analyze the differences between consecutive terms:$8 - 7 = 1 = 1^2$$24 - 8 = 16 = 4^2$$105 - 24

Vedclass · Accepted Answer

$986$

Vedclass · Answer

(A) The given series is $7, 8, 24, 105, 361, ?$.Let's analyze the differences between consecutive terms:$8 - 7 = 1 = 1^2$$24 - 8 = 16 = 4^2$$105 - 24 = 81 = 9^2$$361 - 105 = 256 = 16^2$Observe the pattern in the bases of the squares: $1, 4, 9, 16, 25, ...$These are squares of consecutive integers: $1^2, 2^2, 3^2, 4^2, 5^2, ...$Wait,looking at the differences: $1^2, 4^2, 9^2, 16^2$. The bases are $1^2, 2^2, 3^2, 4^2$. Therefore,the next difference should be $5^2 = 25$,and the square of that difference is $25^2 = 625$.So,the next term is $361 + 625 = 986$.

$264$	$136$	$72$	$40$
$488$	$(a)$	$(b)$	$(c)$

Find the missing number in the series: $7, 8, 24, 105, 361, ?$

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Observe the following table and determine which number will come in place of $(a)$:
$264$ $136$ $72$ $40$
$488$ $(a)$ $(b)$ $(c)$

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