Question

How do you find the `n`th term of the sequence 12, 17, 22, 27, 32?

Answer 1

`n` th term is `a_n= a_1 +(n-1)d`

Explanation:

The sequence is of arithmatic progression

Here 1 st term is `a_1=12` , common difference is

`d=17-12=22-17=5` , n th term is `a_n= a_1 +(n-1)d`

e.g `a_5= 12+(5-1)*5= 12=4*5=32`

So n th term is `a_n= a_1 +(n-1)d` [Ans]

Answer 2

`a_n=5n+7`

Explanation:

`"this is an "color(blue)"arithmetic sequence"`

`"the nth term of the sequence is "`

`•color(white)(x)a_n=a+(n-1)d`

`"where " a" is the first term and d the common difference"`

`"here " a=12" and " d=5`

`rArra_n=12+5(n-1)=5n+7`

`color(blue)"As a check"`

`a_5=(5xx5)+7=32larr" True"`