Question

qual é a soma de todos os múltiplos de 3 compreendidos entre 100 e 200?

Answer 1

102+105+108+111+114+117+120+123+126+129+132+135+138+141+144+147+150+153+156+159+162+165+168+171+174+177+180+183+186+189+192+195+198=4.950

Answer 2

$P.A (102,105,108,111,114,117,120,123,126,129,132,135,138,141,144, \\ 147,150,153,156,159,162,165,168,171,174,177,180,183,186,189,192,\\ 195,198)$

$S_{n} =? \\ a_{1} =102 \\ a_{n} =a_{33}=198 \\ r=3 \\ n=33 \\ \\ \\ S_{n} = \frac{( a_{1} + a_{n} )*n}{2} \\ \\ \\ S_{n} = \frac{(102+198)*33}{2} \\ \\ S_{n} = \frac{300*33}{2} \\ \\ S_{n} = \frac{9900}{2} \\ \\ S_{n} = 4950$