Question

determinati in fiecare caz primul termen si ratia progresiei aritmetice ( a n ) n mai mare sau egal decat 1
a)a1+a4=14,a2+a5=18 b)a2+a4=20,a3+a5=26 c)a3+a4=12,a2+a6=14 d)a1+a4=8,a3+a5=2 e)a3-a2=3 ,a4+a6=28 f)2a3-a1=14,a6=17​

Answer 1

Se foloseste formula: an=a1+(n-1)r , unde r=ratia
a) a1+a1+ 3r=14 => 2a1+3r=14 (1)
a1+a1+4r=18 => 2a1+4r=18 (2)
Scadem relatia (2)-(1) =>ratia r=4
2a1=14-12=2 => primul termen a1=1

b) a1+r+a1+ 3r=20=> 2a1+4r=20 (1)
a1+2r+a1+4r=26> 2a1+6r=26 (2)
Scadem relatia (2)-(1) =>ratia r=6/2=3
2a1=20-12=> primul termen a1=4

c) si d) analog (urmaresc acelasi algoritm de calcul)
e) a1+2r-a1-r=3 =>r=3
a1+3r+a1+5r=28 => 2a1 +24= 28 => a1=2
f) 2a1+ 4r-a1=14 => a1+4r=14 (1)
a1+5r=17 (2)
Din (2)-(1) => r=3
a1=14-12 => a1=2