Question

A soma dos 7 termos iniciais da P.A. (1, 7, 13...) é igual a quanto?
a) 251
b) 14
c) 645
d) 133
e) 850​

Answer 1

$\large\boxed{\begin{array}{l}\rm a_7=a_3+4r\\\rm a_7=13+4\cdot6\\\rm a_7=13+24=37\\\rm s_7=\dfrac{7\cdot(1+37)}{2}\\\\\rm s_7=\dfrac{7\cdot\diagdown\!\!\!\!\!\!38}{\diagdown\!\!\!\!2}\\\\\rm s_7=7\cdot19\\\rm s_7=133\\\huge\boxed{\boxed{\boxed{\boxed{\sf\red{\maltese}~\blue{alternativa~d} }}}}\end{array}}$

Answer 2

Explicação passo-a-passo:

$r = a2 - a1$

$r = 7 - 1$

$r = 6$

_______________

$an = a1 + (an - 1) \times r$

$a7 = 1 + (7 - 1) \times 6$

$a7 = 1 + 6 \times 6$

$a7 = 1 + 36$

$a7 = 37$

________________________

$sn =(a1 + an) \times \dfrac{n}{2}$

$s7 = (1 + 37) \times \dfrac{7}{2}$

$s7 = 38 \times \dfrac{7}{2}$

$s7 = 38 \times 3.5$

s7=133

Opção "D"