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{:[{[g(1)=-5],[g(2)=3],[g(n)=g(n-2)+g(n-1)]:}],[g(3)=◻]:}

{g(1)=−5g(2)=3g(n)=g(n−2)+g(n−1)\begin{cases} g(1) = -5 \\ g(2) = 3 \\ g(n) = g(n-2) + g(n-1) \end{cases} \newlineg(3)=□g(3)=\square

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Domain and range of absolute value functions: equationsright chevron icon

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Q. {g(1)=−5g(2)=3g(n)=g(n−2)+g(n−1)\begin{cases} g(1) = -5 \\ g(2) = 3 \\ g(n) = g(n-2) + g(n-1) \end{cases} \newlineg(3)=□g(3)=\square
  1. Given Recursive Sequence: We are given a recursive sequence for the function g(n)g(n) with the following initial conditions:\newlineg(1)=−5g(1) = -5\newlineg(2)=3g(2) = 3\newlineThe recursive formula for g(n)g(n) is:\newlineg(n)=g(n−2)+g(n−1)g(n) = g(n-2) + g(n-1)\newlineWe need to find the value of g(3)g(3).
  2. Find g(3)g(3): To find g(3)g(3), we use the recursive formula and the initial conditions:\newlineg(3)=g(1)+g(2)g(3) = g(1) + g(2)\newlineWe know that g(1)=−5g(1) = -5 and g(2)=3g(2) = 3, so we substitute these values into the equation:\newlineg(3)=(−5)+3g(3) = (-5) + 3
  3. Calculation and Result: Now we perform the calculation:\newlineg(3)=−5+3g(3) = -5 + 3\newlineg(3)=−2g(3) = -2\newlineSo, the value of g(3)g(3) is −2-2.

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