Two Part Question Bank - Q7

[mukesh.mulchandani]

Following is explanation given for the answer. My question is how can we definitely say that a1 = 3 when it can be -3 as well?

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We’re given a particular sequence: an = (an-1)2 + 1. In regular language, the formula says: to find a particular value (an), take the value of the term just before it in the sequence (an-1), square that value, and add 1.

For example, we’re told that a2 is 10. In order to calculate a3, then, we do this:

a3 = (a2)2 + 1 = (10) 2 + 1 = 100 + 1 = 101. The correct value for a3 is 101.

In order to calculate the correct value for a0, though, we have to work backwards. Try to put the value for a2 in the same form as the formula. The formula is in the form (something + 1):

a2 =10 = 9 + 1

That "something," the 9, was squared in the formula, so next we can write it as:

a2 =10 = 9 + 1 = 32 + 1

Match this up with the original formula:

a2 = 32 + 1

a2 = (a1)2 + 1

The value of a1 must be 3. Repeat this process to find the value of a0:

a1 = 3 = 2 + 1 = (√2) 2 + 1

a1 = (a0)2 + 1

The value of a0 is √2.

[tim]

can you please post the source of the problem, and if the problem is not from a forbidden source, post the entire text of the problem?

to answer your question though, assuming the sequence is defined for all n >= 0, there is no way to get an a_0 if a_1 is -3, so that's how we know it has to be 3..