Find the indicated terms in each of the following sequences whose $n$ th terms are $a_{n} = {(- 1)}^{n} n; a_{3}, a_{5}, a_{8}$

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Solution

The $n^{t h}$ term of the sequence is

$a_{n} = (- 1)^{n} n . . . . . . . . . . . . . . . . . . . e q (1)$

1) To find the third term of sequence $(a_{3})$ put n=3 in eq(1)
$⟹ a_{3} = (- 1)^{3} \times 3$
$⟹ a_{3} = - 1 \times 1$
$⟹ a_{3} = - 3$

2)To find the fifth term of seqence $(a_{5})$ put n=5 in eq(1)
$⟹ a_{5} = (- 1)^{5} \times 5$
$⟹ a_{5} = - 1 \times 5$
$⟹ a_{5} = - 5$

3)To find the eighth term of sequence $(a_{8})$ put n=8 in eq(1)
$⟹ a_{8} = (- 1)^{8} \times 8$
$⟹ a_{8} = 1 \times 8$
$⟹ a_{8} = 8$

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