find an explicit formula for each sequence

Question

1,11,21,31,41,51             dealing with sequences in pre-calculus 

Answer 1

Starting with the second number, each number is 10 more than the number to its left.

 

x₁ = 1

x₂ = 11 = x₁ + 10

x₃ = 21 = x₂ + 10

x₄ = 31 = x₃ + 10

etc.

 

It looks like the pattern is

 

x_n = x_n-1 + 10

 

for n > 1, with x₁ = 1

Answer 2

a_n = 1 + (n - 1)11