Find the indicated terms in each of the following sequences whose $n$ th terms are $a_{n} = \frac{3 n - 2}{4 n + 5}; a_{7}$ and $a_{8}$

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Solution

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

$a_{n} = \frac{3 n - 2}{4 n + 5} . . . . . . . . . . . . . . . . . . . e q (1)$

1) To find the seventh term of sequence $(a_{7})$ put n=7 in eq(1)
$⟹ a_{7} = \frac{3 \times 7 - 2}{4 \times 7 + 5}$
$⟹ a_{7} = \frac{21 - 2}{28 + 5}$
$⟹ a_{7} = \frac{19}{33}$

2)To find the eighth term of sequence $(a_{8})$ put n=8 in eq(1)
$⟹ a_{8} = \frac{3 \times 8 - 2}{4 \times 8 + 5}$
$⟹ a_{8} = \frac{24 - 2}{32 + 5}$
$⟹ a_{8} = \frac{22}{37}$

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