Question

Determine a soma dos 20 primeiros termos de P.A. (27,34,41,...).

Answer 1

$> resolucao \\ \\ \geqslant progressao \: aritmetica \\ \\ > razao \: da \: pa \\ \\ r = a2 - a1 \\ r = 34 - 27 \\ r = 7 \\ \\ > o \: 20 \: termo \: da \: pa \\ \\ an = a1 + (n - 1)r \\ an = 27 + (20 - 1)7 \\ an = 27 + 19 \times 7 \\ an = 27 + 133 \\ an = 160 \\ \\ \geqslant a \: soma \: dos \: termos \: da \: pa \\ \\ sn = \frac{(a1 + an)n}{2} \\ \\ sn = \frac{(27 + 160)20}{2} \\ \\ sn = \frac{187 \times 20}{2} \\ \\ sn = 187 \times 10 \\ \\ sn = 1870 \\ \\ > < > < > < > < > < > < > < > < >$