# How do you write the first five terms of the arithmetic sequence given a_3=19, a_15=-1.7?

Jun 15, 2017

$22.45 , 20.725 , 19 , 17.255 , 15.55$

#### Explanation:

$\text{for a standard arithmetic sequence}$

$\text{the nth term } = a + \left(n - 1\right) d$

$\text{where a is the first term and d the common difference}$

$\text{we require to find both a and d}$

${a}_{3} = a + 2 d = 19 \to \left(1\right)$

${a}_{15} = a + 14 d = - 1.7 \to \left(2\right)$

$\text{subtract "(1)" from } \left(2\right)$

$\Rightarrow 12 d = - 20.7 \Rightarrow d = - 1.725$

$\text{substitute this value in } \left(1\right)$

$a - 3.45 = 19 \Rightarrow a = 22.45$

$\Rightarrow {a}_{1} = 22.45$

${a}_{2} = 22.45 - 1.725 = 20.725$

${a}_{3} = 20.725 - 1.725 = 19$

${a}_{4} = 19 - 1.725 = 17.255$

${a}_{5} = 17.255 - 1.725 - 15.55$