# If a1=5 and a5=15, how do you find the formula for the nth term of the sequence?

Aug 31, 2015

$\textcolor{b l u e}{{a}_{n} = 5 + \left(n - 1\right) \cdot \frac{5}{2}}$

#### Explanation:

a_1 = color(blue)(5
${a}_{5} = 15$

The $n t h$ term is denoted as:

${a}_{n} = {a}_{1} + \left(n - 1\right) d$

So,
${a}_{5} = {a}_{1} + \left(5 - 1\right) \cdot d$

$15 = 5 + 4 d$

$15 - 5 = 4 d$

$10 = 4 d$

$d = \frac{10}{4}$

color(blue)(d=5/2

So the formula for $n t h$ term can now be written as:
${a}_{n} = {a}_{1} + \left(n - 1\right) d$

$\textcolor{b l u e}{{a}_{n} = 5 + \left(n - 1\right) \cdot \frac{5}{2}}$ where $\left(n = 1 , 2 , 3. . .\right)$