Write the first three terms in each of the sequence defined by the following :
(i) $a_{n} = 3 n + 2$
(ii) $a_{n} = n^{2} + 1$

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Solution

(i) We have, $a_{n} = 3 n + 2$

Putting $n = 1, 2$ and $3$ , we get
$a_{1} = 3 \times 1 + 2 = 3 + 2 = 5$
$a_{2} = 3 \times 2 + 2 = 6 + 2 = 8$
$a_{3} = 3 \times 3 + 2 = 9 + 2 = 11$

Thus, the required first three terms of the sequence defined by $a_{n} = 3 n + 2$ are $5, 8$ and $11$ .
(ii) We have $a_{n} = n^{2} + 1$

Putting $n = 1, 2$ and $3$ , we get
$a_{1} = 1^{2} + 1 = 1 + 1 = 2$ ,
$a_{2} = 2^{2} + 1 = 4 + 1 = 5$ ,
and, $a_{3} = 3^{2} + 1 = 9 + 1 = 10$ .

Thus, the first three terms of the sequence defined by $a_{n} = n^{2} + 1$ are $2, 5$ and $10$ .

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Write the first three terms in each of the sequences defined by the following -
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