Find the indicated terms in each of the following sequences whose $n$ th terms are $a_{n} = n (n - 1) (n - 2); a_{5}$ and $a_{8}$

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Solution

The $n^{t h}$ term of the sequence is
$a_{n} = n (n - 1) (n - 2) . . . . . . . . . . . . . . . . . . . e q (1)$
1) To find the fifthth term of sequence $(a_{5})$ put n=5 in eq(1)
$⟹ a_{5} = 5 (5 - 1) (5 - 2)$
$⟹ a_{5} = 5 \times 4 \times 3$
$⟹ a_{5} = 60$
2)To find the eighth term of sequence $(a_{8})$ put n=8 in eq(1)
$⟹ a_{8} = 8 (8 - 1) (8 - 2)$
$⟹ a_{8} = 8 \times 7 \times 6$
$⟹ a_{8} = 336$

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