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# Find the first five terms of the sequence given by a_{1} = 2, a_{2} = 3 + a_{1}and a_{n} = 2a_{n-1} + 5 for n>2.

Answer :

Given that a_{1} = 2, a_{2} = 3 + a_{1} and a_{n} = 2a_{n-1} + 5 for n > 2.

Now, a_{1} = 2

⇒ a_{2} = 3 + a_{1} = 3 + 2 = 5

⇒ a_{3} = 2a_{2} + 5 = 2(5) + 5 = 10 + 5 = 15

⇒ a_{4} = 2a_{3} + 5 = 2(15) + 5 = 30 + 5 = 35

⇒ a_{5} = 2a_{4} + 5 = 2(35) + 5 = 70 + 5 = 75

∴ The required terms of sequence are 2, 5, 15, 35 and 75.

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