$a_{1} = a_{2} = 2, a_{n} = a_{n - 1} - 1, n > 2$

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Solution

$a_{1} = a_{2} = 2, a_{n} = a_{n - 1} - 1, n > 2$
$\Rightarrow a_{3} = a_{2} - 1 = 2 - 1 = 1 a_{4} = a_{3} - 1 = 1 - 1 = 0 a_{5} = a_{4} - 1 = 0 - 1 = - 1$
Hence , the first five terms of the sequence are $2, 2, 1, 0$ and $- 1$ .
Corresponding series is $2 + 2 + 1 + 0 + (- 1) + . . .$

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Similar questions

Write the first five terms in each of the following sequences :

(i) $a_{1} = 1, a_{n} = a_{n - 1} + 2, n > 1$

(ii) $a_{1} = 1 = a_{2}, a_{n} = a_{n - 1} + a_{n} - 2, n > 2$

(iii) $a_{1} = a_{2} = 2, a_{n} = a_{n - 1} - 1, n > 2$

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\frac{a_{1}}{a_{1}} + \frac{a_{2}}{a_{2}} + \frac{a_{3}}{a_{3}} + \dots \frac{a_{n}}{a_{n}} = \frac{1}{1} + \frac{1}{a_{1}} + \frac{a_{1}}{a_{2}} + \frac{a_{2}}{a_{3}} + \dots \frac{a_{n - 2}}{a_{n - 1}}

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