Question

determinado numero de termos da p.a 13 16 19..... 130 133
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Answer 1

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

$\Large\boxed{\begin{array}{l}\underline{\bf Soluc_{\!\!,}\tilde ao}\\\sf \rm PA\,(13,16,19,\dotsc,130,133)\\\sf a_n=133;\, a_1=13;\, r=3;\,n=\,?\\\sf 133= 13+(n-1)\cdot3\\\sf 133=13+3n-3\\\sf 133=10+3n \\\sf 3n=123\\\sf n=\dfrac{123}{3}\\\sf n=41\, termos~\checkmark \end{array}}$