Answer to Question #271352 in Discrete Mathematics for nur

Question #271352

Consider a recurrence relation an = -3an-1 + n for n = 1,2,3,4,… with initial conditions a1 = 3. Calculate a3.

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Expert's answer
2021-11-25T23:44:45-0500

Recurrence relation:

an=3an1+na_{n} = -3a_{n-1} + n

Initial condition:

a1=3a_{1} = 3


Use recurrence relation for n=2n = 2 :

a2=3a1+2=33+2=9+2=7a_{2} = -3a_{1} + 2 = -3 * 3 + 2 =-9 + 2 = -7


Use recurrence relation for n=3n = 3 :

a3=3a2+3=3(7)+3=21+3=24a_{3} = -3a_{2} + 3 = -3 * (-7) + 3 = 21 + 3 = 24


Answer: a3=24a_{3} = 24


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