QUESTION 6
Easy
Let \(T_1 = 1, T_2 = 2, T_3 = 4, \,and\, T_n = T_{n−1} + T_{n−2} + T_{n−3}\) for n ≥ 4. Find \(T_4, T_5, T_6, T_7,\,and\, T_8\).
SOLUTION
1
Note down what is given
\(T_1 = 1,\,T_2 = 2,\,T_3 = 4\)
\(T_n = T_{n−1} + T_{n−2} + T_{n−3}\) for \(n ≥ 4\)
\(T_n = T_{n−1} + T_{n−2} + T_{n−3}\) for \(n ≥ 4\)
2
Find \(T_4\)
\(\begin{aligned} T_4 &= T_3 + T_2 + T_1 \\ &= 4+2+1 \\ &= 7 \end{aligned}\)
3
Find \(T_5\)
\(\begin{aligned} T_5 &= T_4 + T_3 + T_2 \\ &= 7+4+2 \\ &= 13 \end{aligned}\)
4
Find \(T_6\)
\(\begin{aligned} T_6 &= T_5 + T_4 + T_2 \\ &= 13+7+4 \\ &= 24 \end{aligned}\)
5
Find \(T_7\)
\(\begin{aligned} T_7 &= T_6 + T_5 + T_4 \\ &= 24+13+7 \\ &= 44 \end{aligned}\)
6
Find \(T_8\)
\(\begin{aligned} T_8 &= T_7 + T_6 + T_5 \\ &= 44+24+13 \\ &= 81 \end{aligned}\)
🏆
Final Answer : \(T_4 = 7,\,T_5 = 13,\,T_6 = 24,\,T_7 = 44,\,T_8 = 81\)
Concept Note
Some sequences depend on more than one previous term. In this question, each term is the sum of the previous three terms.