1. ## Pre-calc-arithmetic sequence

in an arithmetic sequence t sub 2=6 , t sub 6=16 find t sub 12

sorry i dont know how to do the sub thing.hopefully it makes sense.Thank you!

2. Originally Posted by ep78
in an arithmetic sequence t sub 2=6 , t sub 6=16 find t sub 12

sorry i dont know how to do the sub thing.hopefully it makes sense.Thank you!
see here to see what the variables mean.

since the general term is given by $t_n = t_1 + (n - 1)d$, you have

$t_2 = 6 = t_1 + d$

and

$t_6 = 16 = t_1 + 5d$

you can solve this system for $t_1$ and $d$ and hence find $t_{12} = t_1 + 11d$

3. Originally Posted by ep78
in an arithmetic sequence t sub 2=6 , t sub 6=16 find t sub 12

sorry i dont know how to do the sub thing.hopefully it makes sense.Thank you!
For an arithmetic sequence...

$t_n = t_1 + (n - 1)d$.

You're told that $t_2 = 6$, so

$t_2 = t_1 + (2 - 1)d$

$6 = t_1 + d$

and you're also told that $t_6 = 16$, so

$t_6 = t_1 + (6 - 1)d$

$16 = t_1 + 5d$.

You now have 2 equations in 2 unknowns that you can solve simultaneously. Subtract equation 1 from equation 2 and you should find

$10 = 4d$

$d = \frac{5}{2}$.

Substitute back into equation 1 to get

$6 = t_1 + \frac{5}{2}$

$t_1 = \frac{7}{2}$.

Therefore $t_n = \frac{7}{2} + (n - 1)\frac{5}{2}$.

What is $t_{12}$?