Question

Which number will come next in the sequence 5, 21, 69, 213, 645?

Answer 1

$\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\pink{R}}}}$

${\bf{\green{(5+2)^3=21}}}$

${\bf{\pink{(21+2)^3=69}}}$

${\bf{\orange{(69+2)^3=213}}}$

${\bf{\blue{(213+2)^3=645}}}$

${\bf{\red{(645+2)^3=1941}}}$

${\bf{\green{(1941+2)^3=5829}}}$

Answer 2

The sequence being followed here is :-

Every number is 6 more than thrice the previous number.

eg. 21 = 3×(5) + 6

     69 = 3×(21) + 6

So the next number in the sequence will be

3×(645) + 6

= 1941

So the answer is 1941