Question

3,17,145,1649,? What is the next number?

Answer 1

Explanation:

1power 2+2power1=3

2power3+3power2=17

3 power4+4power3=145

4power5+5power4=1649

5power6+6power5=23401

Answer 2

23401

Mathematical reasoning is a crucial skill that allows peoples to evaluate a hypothesis without having to consider its context or meaning. A factual and scientific foundation is required for derivations and proofs.

Mathematical critical thinking and logical reasoning are essential skills for solving math reasoning problems.  When we study literature, we adhere to particular grammatical principles. A scientific hypothesis, too, has its own set of criteria and components. It's worth noting that most mathematical reasoning books and materials use scientific grammar or applicable terminologies and notations.

In the questuion, the pattern is

$2^{1} + 1^{2}$

$3^{2} + 2^{3}$

$4^{3} + 3^{4}$

$5^{4} + 4^{5}$

$2^{1} + 1^{2}$ = 2+1

           = 2*1 + 1*2

           =  3

$3^{2} + 2^{3}$ = 3*3 + 2*2*2

           = 9+8

           = 17

$4^{3} + 3^{4}$ = 4*4*4 + 3*3*3*3

           = 64 + 81

           = 145

$5^{4} + 4^{5}$ = 5*5*5*5 + 4*4*4*4*4

           = 625 + 1024

           = 1649

Similarly,

$6^{5} + 5^{6}$ = 6*6*6*6*6 + 5*5*5*5*5*5

           = 7776 + 15625

           = 23401

The next number is 23401.