Question

What is the 10th term of the sequence "12, 23, 34, 45...."? How do you write an equation for the `n`th term of the sequence?

Answer 1

For `i=10:color(white)(...) a_10= 111`

So for `i=n:color(white)(...) a_i=a_n=12+11(n-1)`

Explanation:

`color(blue)("Test for Arithmetic")`

{23-12 = 11}, {34-23= 11}, {45-34=11}

This is an Arithmetic sequence as all the differences are the same.

Let `a_i` be the `i"'th term"`

Let n be any integer value

`a_1=12`
`a_2=12+11`
`a_3=12+(2xx11)`
`a_4=12+(3xx11)`

and so on

so if we have `a_i=12+11(i-1)` it should work for any `i`

Test:
`a_1=12+11(1-1) =12`
`a_4=12+11(4-1)=12+33=45`

For `i=10: a_10=12+11(10-1) = 12+99 = 111`

So for `i=n: a_i=a_n=12+11(n-1)`