What is the first term  if  t2=-12 and t5 =9    ( arithmetic)

Expert Answers
lemjay eNotes educator| Certified Educator

To solve, apply the formula of finding the nth term of an arithmetic sequence which is:

`T_n=T_1 + (n-1)d`

where Tn is the nth term, T1 is the first term, and d is the common difference.

Since the T2=-12, then:


`-12=T_1+d`          (Let this be EQ1)

Also, since T5=9, then:


`9=T_1+4d`                  (Let this be EQ2)

Next, use these two equations to solve for the first term T1.

To do so, multiply EQ1 by 4.



Then, subtract this from EQ2.

`-` `-48=4T_1+4d`

Then, divide both sides by -3.



Hence, the first term is -19.