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 $\displaystyle t_n = t_1 + (n - 1)d$, you have
$\displaystyle t_2 = 6 = t_1 + d$
and
$\displaystyle t_6 = 16 = t_1 + 5d$
you can solve this system for $\displaystyle t_1$ and $\displaystyle d$ and hence find $\displaystyle t_{12} = t_1 + 11d$
For an arithmetic sequence...
$\displaystyle t_n = t_1 + (n - 1)d$.
You're told that $\displaystyle t_2 = 6$, so
$\displaystyle t_2 = t_1 + (2 - 1)d$
$\displaystyle 6 = t_1 + d$
and you're also told that $\displaystyle t_6 = 16$, so
$\displaystyle t_6 = t_1 + (6 - 1)d$
$\displaystyle 16 = t_1 + 5d$.
You now have 2 equations in 2 unknowns that you can solve simultaneously. Subtract equation 1 from equation 2 and you should find
$\displaystyle 10 = 4d$
$\displaystyle d = \frac{5}{2}$.
Substitute back into equation 1 to get
$\displaystyle 6 = t_1 + \frac{5}{2}$
$\displaystyle t_1 = \frac{7}{2}$.
Therefore $\displaystyle t_n = \frac{7}{2} + (n - 1)\frac{5}{2}$.
What is $\displaystyle t_{12}$?