Question

What recursive formula can be used to represent the sequence 2,4,6,8,10,...

Answer 1

hello :
10-8=8-6=6-4=4-2=2(common diffrence)of aritmetic sequence
a recursive formula for the sequence is : An+1=An +2

Answer 2

2n

Explanation:

Given the sequence 2,4,6,8,10...

The sequence given is an arithmetic sequence

The nth term of an arithmetic sequence is given as:

Tn = a+(n-1)d where;

a is the first term if the sequence

n is the number of terms

d is the common difference

From the sequence above:

a = 2, d = 4-2 = 6-4 = 8-6 = 2

d = 2

Substituting the given values in the formula we have:

Tn = 2+(n-1)2

Tn = 2+2n-2

Tn = 2n+2-2

Tn = 2n

The recursive formula is Tn = 2n