Question

determine a soma do 20º termo das P.A abaixo:
a) P.A (7, 12, 17...)
b) P.A ( 14, 20...)
c) P.A ( 13, 24, 35...)

Answer 1

Formula da soma da pa: 

$a_n = a_1 + (n-1)~.~r \\\\ S_n = \frac{(a_1 + a_n)~.~n}{2} \\\\ Onde: \\\\ S_n = Soma \\ a_1 = Primeiro~termo \\ a_n = Ultimo~termo \\ n = Numero~de~termos \\ r = Razao$


a) P.A (7, 12, 17...)

$a_{20} = 7 + (20-1)~.~5 \\ a_{20} = 7 + 95 = 102 \\\\ S_{20} = \frac{(7+102).20}{2} = 1090$


b) P.A ( 14, 20...)

$a_{20} = 14 + (20-1)~.~6 \\ a_{20} = 14 + 114 = 228 \\\\ S_{20} = \frac{(14+228).20}{2} = 1420$


c) P.A ( 13, 24, 35...)

$a_{20} = 13 + (20-1)~.~11 \\ a_{20} = 13 + 209 = 222\\\\ S_{20} = \frac{(13+222).20}{2} = 2350$