Question

Identificand un factor comun, in fiecare suma, calculati:
a) 10+20+30+...+1230=
b) 7+14+21+...+315=

Answer 1

a) 10 (1+2+....+123) =10 * (1+123)*123/2 =(10*124*123)/2=10*7626=76260
b) 7(1+2+.....+45)=7*(1+45)*45/2= 7*46*45=7*1035=7245

Answer 2

$\displaystyle a).10+20+30+...+1230=10(1+2+3+...+123)= \\ \\ =10 \cdot \frac{123(123+1) }{2} =10 \cdot \frac{123 \cdot 124}{2} =10 \cdot \frac{15252}{2}=10 \cdot 7626=76260 \\ \\ b).7+14+21+...+315=7(1+2+3+...+45)= \\ \\ =7 \cdot \frac{45(45+1)}{2} =7 \cdot \frac{45 \cdot 46}{2} =7 \cdot \frac{2070}{2} =7 \cdot 1035=7245$