find a formula for an for the arithmetic sequence.
a1=5 , a4=15
ok this is what i did.
an=dn+c and c=a1-d
c=5-d
how do i find d and c???
$\displaystyle a_n = (n-1)d + a_1$
$\displaystyle a_1 = 5, a_4 = (4-1)d + a_1 = (4-1)d + 5 = 15 \Rightarrow 3d + 5 = 15 \Rightarrow 3d = 10 \Rightarrow d = \frac{10}{3}$
Therefore,
$\displaystyle a_n = \frac{10}{3} \cdot (n-1) + 5$
Or in the form you're asked to give:
$\displaystyle a_n = \frac{10}{3} \cdot (n-1) + 5 = \frac{10}{3}n - \frac{10}{3} + 5 = \frac{10}{3}n + \frac{5}{3}$
$\displaystyle a_n = \frac{10}{3}n + \frac{5}{3}$