WISKUNDE
GRAAD 12
NOG OEFENINGE
Rekursiewe formules : antwoorde.
MATHEMATICS
GRADE 12
MORE EXERCISES
Recursive formulae : answers.
1.1 Tn + 1 = Tn + 3
n = 1 : T1 + 1 = T1 + 3
T2 = 8 + 3 = 11
n = 2 : T2 + 1 = T2 + 3
T3 = 11 + 3 = 14
T2 = 11 ; T2 = 14
1.2 Tn + 1 = Tn + 8
n = 1 : T1 + 1 = T1 + 8
T2 = 18 + 8 = 26
n = 2 : T2 + 1 = T2 + 3
T3 = 26 + 8 = 34
T2 = 26 ; T2 = 34
1.3 Tn + 1 = Tn − 5
n = 1 : T1 + 1 = T1 − 5
T2 = 34 − 5 = 29
n = 2 : T2 + 1 = T2 − 5
T3 = 29 − 5 = 24
T2 = 29 ; T2 = 24
1.4 Tn + 1 = Tn + 3
n = 1 : T1 + 1 = T1 + 3
T2 = −18 + 3 = −15
n = 2 : T2 + 1 = T2 + 3
T3 = −15 + 3 = −12
T2 = −15 ; T2 = −12
1.5 Tn + 1 = Tn − 8
n = 1 : T1 + 1 = T1 − 8
T2 = 21 − 8 = 13
n = 2 : T2 + 1 = T2 − 8
T3 = 13 − 8 = 5
T2 = 13 ; T2 = 5
1.6 Tn + 1 = Tn − 9
n = 1 : T1 + 1 = T1 − 9
T2 = 13 − 9 = 4
n = 2 : T2 + 1 = T2 − 9
T3 = 4 − 9 = −5
T2 = 4 ; T2 = −5
1.7 Tn + 2 = Tn + 1 + Tn
n = 1 : T1 + 2 = T1 + 1 + + T1
T3 = T2 + T1
T3 = 7 + 11 = 18
n = 2 : T2 + 2 = T2 + 1 + T2
T4 = 18 + 11 = 29
T3 = 18 ; T4 = 29
1.8 Tn + 2 = Tn + 1 − Tn
n = 1 : T1 + 2 = T1 + 1 − T1
T3 = T2 − T1
T3 = 14 − 18 = −4
n = 2 : T2 + 2 = T2 + 1 − T2
T4 = −4 − 14 = −18
T3 = −4 ; T4 = −18
2.1 18; 23; 28; . . .
T1 = 18
d = T2 − T1
= 23 − 18 = 5
Rekursiewe formule is
Recursive formula is
Tn + 1 = Tn + 5 ; T1 = 18 ; n ≥ 1
2.2 33; 39; 45; . . .
T1 = 33
d = T2 − T1
= 39 − 33 = 6
Rekursiewe formule is
Recursive formula is
Tn + 1 = Tn + 6 ; T1 = 33 ; n ≥ 1
2.3 57; 53; 49; . . .
T1 = 57
d = T2 − T1
= 53 − 57 = −4
Rekursiewe formule is
Recursive formula is
Tn + 1 = Tn − 4 ; T1 = 57 ; n ≥ 1
2.4 35; 29; 23; . . .
T1 = 35
d = T2 − T1
= 29 − 35 = −6
Rekursiewe formule is
Recursive formula is
Tn + 1 = Tn − 6 ; T1 = 35 ; n ≥ 1
2.5 −23; −17; −11; . . .
T1 = −23;
d = T2 − T1
= −17 − (−23) = 6
Rekursiewe formule is
Recursive formula is
Tn + 1 = Tn + 6 ; T1 = −23 ; n ≥ 1
2.6 −3; −8; −13; . . .
T1 = −3
d = T2 − T1
= −8 − (−3) = −5
Rekursiewe formule is
Recursive formula is
Tn + 1 = Tn − 5 ; T1 = −3 ; n ≥ 1