Odpowiedź:
a₂ = a₁ + r
a₇ = a₁ + 6r
a₅ = a₁ + 4r
a₉ = a₁ + 8r
a₂+ a₇ = 20
a₅ + a₉ = 30
a₁ + r + a₁ + 6r = 20
a₁ + 4r + a₁ + 8r = 30
2a₁ + 7r = 20
2a₁ + 12r = 30
Odejmujemy równania
2a₁ - 2a₁ + 7r - 12r = 20 - 30
- 5r = - 10
5r = 10
r = 10/5 = 2
2a₁ + 7r = 20
2a₁ + 7 * 2 = 20
2a₁ + 14 = 20
2a₁ = 20 - 14 =6
a₁ = 6/2 = 3
an = a₁ - (n - 1) * r = 3 - (n - 1) * 2 = 3 - 2n + 2 = - 2n + 5
Odpowiedź:
Szczegółowe wyjaśnienie:
Korzystamy ze wzoru:
[tex]a_n=a_1+(n-1)*r[/tex]
[tex]\left \{ {{a_2+a_7=20} \atop {a_5+a_9=30}} \right. \\\left \{ {{a_1+(2-1)*r+a_1+(7-1)*r=20} \atop {a_1+(5-1)*r+a_1+(9-1)*r=30}} \right. \\\left \{ {{2a_1+r+6r=20} \atop {2a_1+4r+8r=30}} \right. \\\left \{ {{2a_1+7r=20} \atop {2a_1+12r=30}} \right. \\\left \{ {{2a_1+7r=20} \atop {-2a_1-12r=-30}} \right.[/tex]
[tex]-5r=-10\\r=2\\2a_1+7*2=20\\2a_1=20-14\\a_1=3[/tex]
[tex]\left \{ {{a_1=3} \atop {r=2}} \right.[/tex]
Wzór ogólny ciągu to :
[tex]a_n=3+(n-1)*2=3+2n[/tex]