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

##### 1 Answer

Jun 26, 2017

#### 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#