Q. If f(1)=7 and f(n)=2f(n−1)−2 then find the value of f(3).Answer:
Find f(2): We are given the initial condition f(1)=7 and the recursive formula f(n)=2f(n−1)−2. To find f(3), we first need to find f(2) using the recursive formula.Using the formula, we substitute n=2 to find f(2):f(2)=2f(2−1)−2f(2)=2f(1)−2f(2)=2×7−2f(1)=70f(1)=71
Find f(3): Now that we have f(2), we can use it to find f(3) using the same recursive formula.Substitute n=3 into the formula to find f(3):f(3)=2f(3−1)−2f(3)=2f(2)−2f(3)=2×12−2f(3)=24−2f(3)=22
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