explicit formula for 2 4 6 8

Question

i am trying to find a recursive and explicit formula for the pattern 2,4,6,8

Answer 1

Explicit Formula of a Sequence  -  A formula that allows direct computation of any term for a sequence a₁, a₂, a₃, . . . , a_n, . . . .  Thus, given an n, we can immediately determine a_n.

 

Note that this is an arithmetic sequence, so the explicit formula is:

  a_n = a₁ + (n-1)d      where a₁ is the first term and d is the common difference

 

  a_n = 2 +(n-1)2

  a_n = 2 + 2n - 2

  a_n = 2n

 

 

Recursive Formula of a Sequence

For a sequence a₁, a₂, a₃, . . . , a_n, . . . a recursive formula is a formula that requires the computation of all previous terms in order to find the value of a_n.

 

The recursive definition for this sequence is:

       a₁ = 2                                              [base case]

       a_n = a_n-1 + 2             for n>1          [recursive case]