Question

Calculati:
a) a-2a+3a-4a+....+49a-50a
b) (-15a)-(10a)+(5a)+(3a)-17a
c) -a-4a-7a-...-103a

Answer 1

a) (a-2a)+(3a-4a)+................+(49a-50a) = (-1)·50 = - 50
b) -15a - 10a + 5a + 3a - 17a = -34a
c) - a(1+4+7 + .............+103) = -a[ (1+3·0) + (1+3·1) + (1+3·2) +......+(1+3·34)] =
= -a[1·35 + 3·(1+2+3+..........+34)] = -a[35 +3·34·35/2] = -35a·(1+ 3·17) = - 1820a