Question

the first term in an arithmetic sequence is 3. The fourth term in the sequence is 21. The tenth term is 57. Create a function that can be used to find the nth term of the arithmetic sequence.

Answer 1

a[n] = 6n -3

Explanation:

The n-th term of an arithmetic sequence with first term a[1] and common difference d can be written as ...

... a[n] = a[1] + (n-1)·d

We can use any of the given terms to find d, and so find the n-th term.

... a[4] = 21 = 3 + (4-1)d

... 18/3 = d = 6 . . . . . subtract 3, divide by 3

So, the n-th term is ...

... a[n] = 3 + (n-1)·6 = 3 + 6n - 6

... a[n] = 6n -3

_____

Check

a[1] = 6·1 - 3 = 3 . . . yes

a[4] = 6·4 -3 = 21 . . . yes

a[10] = 6·10 -3 = 57 . . . yes