Which function describes the sequence 1,6,11,16,21,…

Answer 1

What you have there is an Arithmetic Sequence that starts at 1 and 5 is added every time. So for your sequence 1, 6, 11, 16, 21, start at 1 and add five to get 6, then add five again to get 11, again to get 16 and so on. If you want to continue the sequence beyond 21, add 5 and you will get 26. I'll let you expand it further if you want.

Answer 2

A sequence is a list of items/objects which have been arranged in a sequential way.

The sequence, 1,6,11,16,21 ... appears to be an Arithmetic Sequence with a Common Difference of 5.

You may write that sequence using an Explicit formula (where the n^th term uses n to determine its value) or using a Recursive formula (where previous values in the sequence is/are used to determine this value).

Explicit formula:

A₁ = 1

A_n = 1 + 5(n-1) for n > 1

( note: this is also A_n = 5n - 4 )

Recursive formula

A₁ = 1

A_n = A_n-1 + 5 for n > 1