Nth Term Equivalent Expression

Question

Hi all

 

Can you explain to me why 4(2^n + 2^(n-1)) is equivalent to 2^(n+2)+2^(n+1) ?

 

Thanks

 

Jim

Answer 1

4(2^n+2^(n-1))=2^(n+2)+2^(n+1)

4=2^2

(2^2)(2^n+2^(n-1))=

(2^2)(2^n)+(2^2)(2^(n-1))=

2^(n+2)+2^(2+n-1)=

2^(n+2)+2^(n+1) which is the right side

4=2^2 and when you multiply with the same bases you add the exponents

Answer 2

4(2ⁿ + 2^n-1) = 4(2ⁿ) + 4(2^n-1)

 

                   = 2²2ⁿ + 2²2^n-1

 

                   = 2ⁿ⁺² + 2ⁿ⁺¹