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If a_(1)=4 and a_(n)=(a_(n-1))^(2)+2 then find the value of a_(3). Answer:

If a1=4 a_{1}=4 and an=(an−1)2+2 a_{n}=\left(a_{n-1}\right)^{2}+2 then find the value of a3 a_{3} .\newlineAnswer:

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Composition of linear and quadratic functions: find a valueright chevron icon

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Q. If a1=4 a_{1}=4 and an=(an−1)2+2 a_{n}=\left(a_{n-1}\right)^{2}+2 then find the value of a3 a_{3} .\newlineAnswer:
  1. Find a2a_{2} Value: Determine the value of a2a_{2} using the recursive formula.\newlineWe know that a1=4a_{1} = 4. To find a2a_{2}, we use the formula an=(an−1)2+2a_{n} = (a_{n-1})^2 + 2 with n=2n=2.\newlinea2=(a1)2+2=42+2=16+2=18a_{2} = (a_{1})^2 + 2 = 4^2 + 2 = 16 + 2 = 18.
  2. Calculate a3a_{3} Value: Determine the value of a3a_{3} using the recursive formula.\newlineNow that we have a2=18a_{2} = 18, we can find a3a_{3} using the same formula an=(an−1)2+2a_{n} = (a_{n-1})^2 + 2 with n=3n=3.\newlinea3=(a2)2+2=182+2=324+2=326a_{3} = (a_{2})^2 + 2 = 18^2 + 2 = 324 + 2 = 326.

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