Q5 of 110 Page 37

Find the first five terms of the sequence given by a1 = 2, a2 = 3 + a1and an = 2an-1 + 5 for n>2.

Given that a1 = 2, a2 = 3 + a1 and an = 2an-1 + 5 for n > 2.


Now, a1 = 2


⇒ a2 = 3 + a1 = 3 + 2 = 5


⇒ a3 = 2a2 + 5 = 2(5) + 5 = 10 + 5 = 15


⇒ a4 = 2a3 + 5 = 2(15) + 5 = 30 + 5 = 35


⇒ a5 = 2a4 + 5 = 2(35) + 5 = 70 + 5 = 75


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


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