Question

How do you write a rule for the nth term of the arithmetic sequence `a_8=19/5, a_12=27/5`?

Answer 1

`a_n=2/5n+3/5`

Explanation:

For the standard `color(blue)"arithmetic sequence"`

`a,a+d,a+2d,a+3d,........,`

The nth term is `• a_n=a+(n-1)d`

where a is the first term and d, the common difference.

For the sequence in question we have to find a and d

`rArra_8=a+7d=19/5to(color(red)(1))`

`rArra_(12)=a+11d=27/5to(color(red)(2))`

`(color(red)(2))-(color(red)(1))` gives d

`rArr4d=8/5rArrd=2/5`

Substitute this value into `(color(red)(1))`

`rArra+14/5=19/5rArra=1`

We can now obtain the nth term rule.

`rArra_n=1+2/5(n-1)`

`rArra_n=2/5n+3/5larrcolor(red)" nth term rule"`