Question

Here are the first four terms of an arithmetic sequence. 5 11 17 23 Write down an expression, in terms of n , for the nth term of the sequence.

Answer 1

To find the expression for the nth term of the sequence, we need to first find the common difference.

The common difference is the difference between any two consecutive terms in the sequence. We can see that the difference between each pair of consecutive terms is 6. Therefore, the common difference is 6.

To find the nth term, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

Substituting the values we have:

a1 = 5

d = 6

So the expression for the nth term of the sequence is:

an = 5 + (n - 1)6

Simplifying:

an = 6n - 1