Question

Se considera sirurile 2010,2006,2002,...,2 si 2010,2002,1994,...2. Determinati nr. termenilor fiecarui sir. Determinati cati termeni comuni au cele doua siruri.

Answer 1

Primul sir contine nr de forma 4k+2, adica multipli de 4 plus 2.
2=4*0+2
.
.
.
2006=4*501+2
2010=4*502+2
=> Avem 503 termeni.

Al doilea sir contine multipli de 4k+2,din 2 in 2.
2010=4*502+2
2002=4*500+2
1994=4*498+2
.
.
.
2=4*0+2
=>Avem 502:2+1=252 termeni