Write the first five terms in each of the following sequence:
$a_{1} = 1 = a_{2}, a_{n - 1} + a_{n - 2}, n > 2$

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Solution

$\begin{matrix} a_{1} = a_{2} = 1 a (n) = a_{n - 1} + a_{n - 2} n > 2 s o, p u t n = 3 a (3) = a_{3 - 1} + a_{3 - 2} = a_{2} + a_{1} = 1 + 1 = 2 p u t n = 4 a (4) = a_{4 - 1} + a_{4 - 2} = a_{3} + a_{2} = 2 + 1 = 3 p u t n = 5 a (5) = a_{5 - 1} + a_{5 - 2} = a_{4} + a_{3} = 3 + 2 = 5 s o, f i r s t f i v e t e r m s a r e a_{1} = 1 a_{2} = 1 a_{3} = 2 a_{4} = 3 a_{5} = 5 \end{matrix}$

Hence, this is the answer.

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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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