Ramos Gordon
10/31/2023 · High School
(d) Consider the quadratic number pattern: \( 2 ; 3 ; 6 ; 11 ; \ldots \) \( \begin{array}{ll}\text { (1) Determine the } 5^{\text {th }} \text { term. } & \text { (2) Determine the general term }\left(T_{n}\right) \\ \text { (3) Determine the } 50^{\text {th }} \text { term. } & \text { (4) Which term is equal to } 443 \text { ? } \\ \text { (e) Given the quadratic number pattern: } 3 ; 3 ; 4 ; 6 ; \ldots \text { Determine } \\ \text { (1) a formula for the } n \text {-th term. } & \text { (2) } T_{100} \\ \text { (3) the value of } k \text { if } T_{k}=94 . & \end{array} \)
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- Part (d):
1. 5th term: 18
2. General term: \( T_n = n^2 - 2n + 3 \)
3. 50th term: 2403
4. Term equal to 443: 22
- Part (e):
1. Formula for \( n \)-th term: \( T_n = \frac{1}{2}n^2 - \frac{3}{2}n + 4 \)
2. 100th term: 4854
3. \( k \) if \( T_k = 94 \): \( k \) needs to be calculated.
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