## What will be the next number in below sequence?

0, 1, 5, 19, 65, 211, ?

Check your answer:-

explanation:

it follows this equation

**3^n – 2^n**where n is integer starting from 0

thus

3^0 – 2^0 = 1 – 1 = 0

3^1 – 2^1 = 3 – 2 = 1

3^2 – 2^2 = 9 – 4 = 5

3^3 – 2^3 = 27 – 8 = 19

3^4 – 2^4 = 65

3^5 – 2^5 = 211

3^6 – 2^6 = 729 – 64 = 665

There is one more way to solve this

**3*previous number + 2^(n-1)**

0x3+1=1;

1×3+2=5;

5×3+4=19;

19×3+8=65;

65×3+16=211;

211×3+32=665;

**wondering how it is possible?**

lets solve 3*previous number + 2^(n-1)

=> 3*(3^(n-1) – 2^(n-1)) + 2^(n-1)

=> 3^n – (2+1)*2^(n-1) + 2^(n-1)

=> 3^n – 2^n – 2^(n-1) + 2^(n-1)

=> 3^n – 2^n i.e. our first equation