Question

Let n represent the position of a term in the sequence below.

8, 11, 14, 17, 20, 23,

Which algebraic expression can be used to find the nth term of the sequence

Answer 1

The algebraic expression can be used to find the nth term of the sequence is:

`a_n = 5+3n`

Where,
`n\geq 1` and n is a positive whole number

Solution:

Given sequence is:

8, 11, 14, 17, 20, 23

Let us find the common difference between terms

11 - 8 = 3

14 - 11 = 3

17 - 14 = 3

20 - 17 = 3

23 - 20 = 3

Thus the common difference between successive term and previous term is constant

Thus this is a arithmetic sequence

The formula for nth term term of arithmetic sequence is given as:

`a_n = a_1+(n-1)d`

Where,

`a_n` is the nth term of sequence

`a_1` is the first term of sequence

d is the common difference between terms

Here in this sequence, 8, 11, 14, 17, 20, 23

`a_1 = 8\\\\d = 3`

Therefore,

`a_n = 8+(n-1)3\\\\a_n = 8+3n -3\\\\a_n = 5+3n`

Where,
`n\geq 1` and n is a positive whole number

Thus algebraic expression can be used to find the nth term of the sequence is found