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

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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.**