Question

1 - Dada a PA (3, 10, 17, 24, ...), determine qual será o 100º termo.


2 - Calcule a soma dos 50 últimos termos da PA da questão número 1.​

Answer 1

$\large\boxed{\begin{array}{l}\sf 1)\\\begin{cases}\rm a_1=3\\\rm r=10-3=7\\\rm a_{100}=?\end{cases}\\\rm a_{100}=a_4+96r\\\rm a_{100}=24+96\cdot7\\\rm a_{100}=24+672\\\rm a_{100}=696\\\sf 2)\\\rm a_{50}=a_4+46r\\\rm a_{50}=24+46\cdot7\\\rm a_{50}= 24+322\\\rm a_{50}=346\\\rm S_{50}=\dfrac{\diagdown\!\!\!\!\!\!\!\!\!50\cdot(346+3)}{\diagdown\!\!\!\!\!2}\\\\\rm S_{50}=25\cdot349\\\rm S_{50}=8725\end{array}}$