Let T1 = 1, T2 = 2, T3 = 4, and Tn = Tn-1 + Tn-2 + Tn-3 for n ≥ 4. Class 9

Let T1 = 1, T2 = 2, T3 = 4, and Tn = Tn-1 + Tn-2 + Tn-3 for n ≥ 4. Class 9

Question 1.

Let T₁ = 1, T₂ = 2, T₃ = 4, and T_n = T_n-1 + T_n-2 + T_n-3 for n ≥ 4. Class 9

Find T₄, T₅ T₆, T₇, and T₈.

Solution:

Given,

T₁ = 1, T₂ = 2, T₃ = 4 and

T_n = T_n-1 + T_n-2 + T_n-3 for n ≥ 4

Substituting n = 4, 5, 6, 7, and 8 in the given recursive rule, we get

T₄ = T₃ + T₂ + T₁ = 4 + 2 + 1 = 7

T₅ = T₄ + T₃ + T₂ = 7 + 4 + 2 = 13

T₆ = T₅ + T₄ + T₃ = 13 + 7 + 4 = 24

T₇ = T₆ + T₅ + T₄ = 24 +13 + 7 = 44

T₈ = T₇ + T₆ + T₅ = 44 + 24 + 13 = 81

∴ Required terms are 7, 13, 24, 44, 81.