# (Homework Solution): PROBLEM 3 [points.151 Sequence {an} defined as follows. ao = 1 a11 anan-1 an-2+ 2

PROBLEM 3 [points.151 Sequence {an} defined as follows. ao = 1 a11 anan-1 an-2+ 2 where n 2 2 What are. a2,a3,a4?

The answer is so simple. Just replace the values:

Given that: a0=1 and a1=1 and

an=an-1 . an-2 +2 where n>=2—————–> (1)

Finding a2:

Place n=2 in equation-(1)

we get, a2=a2-1 a2-2 + 2

that is a2=a1 a0 +2 (substitute a1 =1 and a0=1 )

we get a2=(1)(1)+2 = 1+2 = 3

Hence a2=3

Finding a3:

Place n=3 in equation-(1)

we get, a3=a3-1 a3-2 + 2

that is a3=a2 a1 +2   (substitute a1 =1 and a2=3 )

we get  a3=(3)(1)+2 = 3+2 = 5

Hence a3=5.

Finding a4:

Place n=4 in equation-(1)

we get, a4=a4-1 a4-2 + 2

that is a4=a3 a2 +2   (substitute a3 =5 and a2=3 )

we get  a4=(5)(3)+2 = 15+2 = 17

Hence a4=17.

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SO THE SOLUTIONS ARE:

• a2=3
• a3=5
• a4=17

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