Question

How do you find an equation that describes the sequence `7, 10, 13, 16,...` and find the 89th term?

Answer 1

Arithmatic sequene with common diference `3` and
`89` th term is `271`

Explanation:

This is an arithmatic sequene , the common difference is

`d=16-13=13-10=10-7=3 ; 1`st term is `a=7`

`n` th term is `t_n=a+(n-1)d :. 89` th term is

`t_89=7+(89-1)3= 7+264=271`

`89` th term is `271` [Ans]

Answer 2

`a_n=3n+4,a_(89)=271`

Explanation:

`"the given terms are the terms of an "color(blue)"arithmetic sequence"`

`a,a+d,a+2d,a+3d,...... ,a+(n-1)d`

`"where a is the first term and d the "color(blue)"common difference"`

`d=a_2-a_1=a_3-a_2=......=a_n-a_(n-1)`

`"here "d= 10-7=13-10=16-13=3`

`"the nth term of the sequence is"`

`•color(white)(x)a_n=a+(n-1)d`

`rArra_n=7+3(n-1)=7+3n-3`

`rArra_n=3n+4larrcolor(red)"nth term formula for sequence"`

`rArra_(89)=(3xx89)+4=271`