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# Find the first six terms of the sequence given by

a_{1} = a_{2} = a_{3} = 1 and a_{n} = a_{n-1} + a_{n-2} for n >3.

Answer :

Given that a_{1} = a_{2} = a_{3} = 1 and a_{n} = a_{n-1} + a_{n-2} for n > 3.

Now, a_{1} = 1

⇒ a_{2} = 1

⇒ a_{3} = 1

⇒ a_{4} = a_{3} + a_{2} = 1 + 1 = 2

⇒ a_{5} = a_{4} + a_{3} = 2 + 1 = 3

⇒ a_{6} = a_{5} + a_{4} = 3 + 2 = 5

∴ The required terms of the sequence are 1, 1, 1, 2, 3 and 5.

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