Bonjour,
(Un) suite arithmétique de raison r et de 1er terme U₀
⇒ Un = U₀ + nr
⇒ U₀ = Un - nr
a) U₁ = 2 et r = -3
U₀ = U₁ - 1x(-3) = 2 + 3 = 5
U₁₆ = U₀ + 16r = 5 - 16x3 = -43
b) U₂ = 13 et r = -1,5
U₀ = U₂ - 2r = 13 + 3 = 15
U₁ = U₀ + r = 15 - 1,5 = 13,5
U₁₆ = U₀ + 16r = 15 - 16x1.5 = -9
c) U₃₁ = 17 et r = -3/2
U₀ = U₃₁ - 31r = 17 - 31x3/2 = 34/2 - 93/2 = -59/2
U₁ = U₀ + r = -59/2 - 3/2 = -62/2 = -31
U₁₆ = U₀ + 16r = -59/2 - 16x3/2 = -107/2
d) U₉ = 11/3 et r = 4/3
U₀ = U₉ - 9r = 11/3 - 36/3 = -25/3
U₁ = U₀ + r = -25/3 + 4/3 = -21/3 = -7
U₁₆ = U₀ + 16r = -25/3 + 64/3 = 39/3= 13
