Problem

If \( a_{1}=2 \) and \( a_{n}=\left(a_{n-1}\right)^{2}-2 \) then find the value of \( a_{4} \).
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Answer

a_4 = (a_3)^2 - 2 = (2)^2 - 2 = 2

Steps

Step 1 :a_2 = (a_1)^2 - 2 = (2)^2 - 2 = 2

Step 2 :a_3 = (a_2)^2 - 2 = (2)^2 - 2 = 2

Step 3 :a_4 = (a_3)^2 - 2 = (2)^2 - 2 = 2

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