The sum of the first $n$ terms of the series $T$ is given by $2n^3 - 8n^2 - 4n$. Find an expre

Question

The sum of the first $n$ terms of the series $T$ is given by $2n^3 - 8n^2 - 4n$. Find an expression for $t_n$, the $n$th term of series $T$.[2] The $n$th term of the series $U$ is given by $u_n = 50n - 204$. Find the values of $n$ for which $u_n = t_n$.[2] The $n$th term of the series $V$ is given by $v_n = 3n + 16$. Find the smallest number greater than $100$ that is in both series $U$ and series $V$.[2] The $n$th term of the series $W$ is given by $w_n = 3n^2 - 5n + 7$. Explain why all the terms in series $W$ are odd numbers.[2] Hence explain why series $U$ and series $W$ do not have any terms in common.[1]

Accepted Answer

(a) $t_n=6n^2-22n+6$ (b) $n=5$ or $n=7$ (c) $196$ (d)(i) Every term of $W$ is odd (ii) $U$ and $W$ have no terms in common

N2024 P2 Q4

N2024 P2 Q4

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