Find the next number in the series: 14, 15, 2 | vedclass

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Question

(A) Observe the pattern of differences between consecutive terms:$15 - 14 = 1 = 1^2$$23 - 15 = 8$ (This does not follow the square pattern directly).L

Vedclass · Accepted Answer

$121$

Vedclass · Answer

(A) Observe the pattern of differences between consecutive terms:$15 - 14 = 1 = 1^2$$23 - 15 = 8$ (This does not follow the square pattern directly).Let us re-examine the series: $14, 15, 23, 32, 96, ?$$14 + 1^3 = 15$$15 + 2^3 = 23$$23 + 3^2 = 32$$32 + 4^2 = 48$ (Wait,the series provided is $14, 15, 23, 32, 96, ?$).Actually,the pattern is: $14 + 1^2 = 15$,$15 + 2^3 = 23$,$23 + 3^2 = 32$,$32 + 4^3 = 96$,$96 + 5^2 = 121$.The pattern alternates between adding the square and the cube of consecutive integers: $1^2, 2^3, 3^2, 4^3, 5^2$.Therefore,the next term is $96 + 5^2 = 96 + 25 = 121$.

$8$	$8$	$12$	$24$
$36$	$(A)$	$(B)$	$(C)$	$(D)$	$(E)$

$12$	$28$	$64$	$140$
$37$	$(a)$	$(b)$	$(c)$	$(d)$	$(e)$

Find the next number in the series: $14, 15, 23, 32, 96, ?$

Similar Questions

Observe the pattern in the table below and determine which number will come in place of $(E)$:
$8$ $8$ $12$ $24$
$36$ $(A)$ $(B)$ $(C)$ $(D)$ $(E)$

Observe the following table and determine the value that should replace $(e)$:

$12$ $28$ $64$ $140$

$37$ $(a)$ $(b)$ $(c)$ $(d)$ $(e)$

Find the next number in the series: $3, 100, 297, 594, 991, ?$

What is the sum of the first $13$ terms of an arithmetic progression if the first term is $-10$ and the last term is $26$?

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

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