# Thread: Arithmetic sequence

1. ## Arithmetic sequence

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???

2. $a_n = (n-1)d + a_1$

$a_1 = 5, a_4 = (4-1)d + a_1 = (4-1)d + 5 = 15 \Rightarrow 3d + 5 = 15 \Rightarrow 3d = 10 \Rightarrow d = \frac{10}{3}$

Therefore,

$a_n = \frac{10}{3} \cdot (n-1) + 5$

Or in the form you're asked to give:

$a_n = \frac{10}{3} \cdot (n-1) + 5 = \frac{10}{3}n - \frac{10}{3} + 5 = \frac{10}{3}n + \frac{5}{3}$

$a_n = \frac{10}{3}n + \frac{5}{3}$