Question

2

Here are the first five terms of an arithmetic
sequence: 1, 6, 11, 16, 21, ...
a Write down, in terms of n, an expression for
the nth term of this arithmetic sequence.

Answer 1

The common difference of this arithmetic sequence is 5, since each term is 5 more than the previous term.

Therefore, the nth term of this arithmetic sequence can be expressed as:

a_n = 1 + (n-1)d

where a_n is the nth term of the sequence, n is the term number, and d is the common difference.

Substituting the values of the first term and the common difference, we get:

a_n = 1 + (n-1)5

Simplifying this expression, we get:

a_n = 5n - 4

Therefore, the expression for the nth term of this arithmetic sequence is 5n - 4.