Question

O primeiro termo de uma Pa é 100 e a30 é 187. Qual a soma dos Trinta primeiro termos​

Answer 1

Resposta:

Sn = ( a1 + an ) n / 2

Sn = ( 100 + 187 ) 30 / 2

Sn = 287 * 30 / 2

Sn = 8610 / 2

Sn = 4305

Answer 2

$\large\boxed{\begin{array}{l}\underline{\rm Soma~dos~termos~de~uma~PA}\\\huge\boxed{\boxed{\boxed{\boxed{\sf S_n=\dfrac{n\cdot(a_1+a_n)}{2}}}}}\\\sf S_n\longrightarrow soma~dos~termos\\\sf n\longrightarrow n\acute umero~de~termos\\\sf a_1\longrightarrow 1^o~termo\end{array}}$

$\large\boxed{\begin{array}{l}\tt dados\begin{cases}\sf a_1=100\\\sf a_n=a_{30}=187\\\sf n=30\\\sf S_{30}=?\end{cases}\\\underline{\rm soluc_{\!\!,}\tilde ao:}\\\sf S_n=\dfrac{n\cdot(a_1+a_n)}{2}\\\sf S_{30}=\dfrac{\diagdown\!\!\!\!\!\!30\cdot(100+187)}{\backslash\!\!\!\!2}\\\sf S_{30}=15\cdot287\\\sf S_{30}=4305\end{array}}$