Question

Determine o décimo sétimo termo da P.A. (-6, -1, 4, ...).

Answer 1

$<var>R = -1-(-6) \\ R = -1+6 = \boxed{5}</var>$

 

$<var>a_{1} = -6</var>$

 

 

 

$<var>a_{n} = a_{1} + (n-1) \cdot R \\\\ a_{17} = -6 + (17-1) \cdot 5 \\\\ a_{17} = -6 + 16 \cdot 5 \\\\ a_{17} = -6 + 80 \\\\ \boxed{\boxed{a_{17} = 74}}</var>$

Answer 2

Observe que:

 

$\text{r}=\text{a}_3-\text{a}_2=\text{a}_2-\text{a}_1=4-(-1)=-1-(-6)=5$

 

Note que:

 

$\text{a}_{\text{n}}=\text{a}_1+(\text{n}-1)\cdot\text{r}$

 

Logo:

 

$\text{a}_{17}=-6+(17-1)\cdot5$

 

$\text{a}_{17}=-6+80=74$

 

Desta maneira, o décimo sétimo termo da P.A. (-6, -1, 4, ...) é 74.