Question

1- Qual o quinquagésimo termo da P.A (3,7....)​

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Progress\tilde ao ~Aritm\acute etica}\\\huge\boxed{\boxed{\boxed{\boxed{\sf a_n=a_1+(n-1)\cdot r}}}}\\\sf a_n\longrightarrow en\acute esimo~ termo\\\sf a_1\longrightarrow primeiro~ termo\\\sf n\longrightarrow n\acute umero~ de~ termos\\\sf r\longrightarrow raz\tilde ao \end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\bf Soluc_{\!\!,}\tilde ao}\\\sf \rm PA\,(3,7,\dotsc)\\\sf a_1=3;\, r=4;\,n=50;\,a_{50}=\,?\\\sf a_{50}=3+(50-1)\cdot4\\\sf a_{50}=3+49\cdot4\\\sf a_{50}=3+ 196\\\sf a_{50}= 199~\checkmark \end{array}}$

Answer 2

Vamos lá.

PA

a1 = 3

a2 = 7

razão

r = a2 - a1

r = 7 - 3 = 4

termo geral

an = a1 + r*(n - 1)

an = 3 + 4n - 4

an = 4n - 1

termo a50

a50 = 4*50 - 1

a50 = 199