Homework Help

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

user profile pic

babylove12 | Student, Grade 10 | eNoter

Posted June 14, 2013 at 1:18 AM via web

dislike 1 like

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

1 Answer | Add Yours

user profile pic

Mary Joy Ripalda | High School Teacher | (Level 3) Educator

Posted June 14, 2013 at 3:30 AM (Answer #1)

dislike 1 like

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:

`T_2=T_1+(2-1)d`

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

Also, since T5=9, then:

`T_5=T_1+(5-1)d`

`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.

`4(-12=T_1+d)`

`-48=4T_1+4d`

Then, subtract this from EQ2.

         `9=T_1+4d`
`-` `-48=4T_1+4d`
`------------`
      `57=-3T_1`

Then, divide both sides by -3.

`57/(-3)=(-3T_1)/(-3)`

`-19=T_1`

Hence, the first term is -19.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes