Question

How do you write a rule for the nth term of the arithmetic sequence `a_6=43, a_15=107.8`?

Answer 1

`a_n=7.2n-0.2`

Explanation:

`"the nth term formula for an arithmetic sequence is"`

`• a_n=a_1+(n-1)d`

`"where " a_1" is the first term and d the common difference"`

`a_1" and d require to be found"`

`"using the "color(blue)"nth term formula"`

`a_6=a_1+5d=43 to(1)`

`a_(15)=a_1+14d =107.8to(2)`

`(2)-(1)`

`rArr9d=64.8`

`rArrd=7.2`

`"substitute this value in " (1)" and solve for " a_1`

`a_1=43-(5xx7.2)=7`

`rArra_n=7+(n-1)7.2`

`rArra_n=7.2n-0.2`