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 $96 + 5^2 = 96 + 25 = 121$.

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

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