Question

14, 39, 84, 155, 258, ____
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Answer 1

I hope the answer is : 399

i have mentioned my logic on the paper ✌️✌️

HOPE THIS HELPS YOU ✌️✌️☘️☘️

Answer 2

Given,

14, 39, 84, 155, 258, ____

To Find,

The next term =?

Solution,

We can find the next term as follows:

Taking the first term,

$2^{3} + 2^{2} + 2 = 8 + 4 + 2 = 14$

Taking the second term,

$3^{3} + 3^{2} + 3 = 27 + 9 + 3 = 39$

Taking the third term,

$4^{3} + 4^{2} + 4 = 64 + 16 + 4 = 84$

Taking the fourth term,

$5^{3} + 5^{2} + 5 = 125 + 25 + 5 = 155$

Taking the fifth term,

$6^{3} + 6^{2} + 6 = 216 + 36 + 6 = 258$

Now,

The following series clearly follows a pattern: $(n + 1)^{3} + (n + 1)^{2} + (n + 1)$.

The next term will be,

$7^{3} + 7^{2} + 7 = 343 + 49 + 7 = 399$

Hence, the next term is 399.