Se considera sirul de triplete:
( 47,48,3) , ( 49,50,9),( 51,52,15) ,(53,54,21),(55,56,27)
a ) sa se determine urmatoarele 2 triplete din sir (57,58,33),(59,60,39)
b ) determinati al 984-lea termen
c ) sa se determine toate tripletele care contin numarul 2013
Justificati raspunsurile .
Se considera sirul de triplete:
(50,52,10) , (53,55,17) , (56,58,24) , (59,61,31) , (62,64,38)
a ) sa se determine urmatoarele 2 triplete din sir
Formula este (a,b,c),(a+3,b+3,c+7) deci urmatoarele 2 triplete sunt:
(62+3, 64+3, 38+7)=(65,67,45)
(65+3,67+3,45+7)=(68,70,52)
b ) determinati al 1000-lea termen
1(47+3*1, 49+3*1, 3+7*1)=(50,52,10)
2…(47+3*2, 49+3*2, 3+7*2)=(53,55,17)
3…(47+3*3, 49+3*3, 3+7*3)=(56,58,24)
4…(47+3*4, 49+3*4, 3+7*4)=(59,61,31)
5…(47+3*5, 49+3*5, 3+7*5)=(62,64,38)
6…(47+3*6, 49+3*6, 3+7*6)=(65,67,45)
7…(47+3*7, 49+3*7, 3+7*7)=(68,70,52)
…….
1000(47+3*1000, 49+3*1000, 3+7*1000)=(3047, 3049, 7003)
c ) sa se determine toate tripletele care contin numarul 2012
47+3*x=2012 , 3*x=1965 , x=655, rezulta tripleta (47+3*655, 49+3*655, 3+7*655) = (2012, 2014, 4588)
49+3*x=2012, 3*x=1963, x nu este nr natural.
3+7*x=2012, 7*x=2009, x=287, rezulta tripleta (47+3*287, 49+3*287, 3+7*287) = (908,910,2012)