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g(n)=-50-15 n Complete the recursive formula of g(n). g(1)= g(n)=g(n-1)+

g(n)=−50−15n g(n)=-50-15 n \newlineComplete the recursive formula of g(n) g(n) .\newline g(1) = \(\square\) \newline g(n) = g(n-1)+\(\square\)

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Q. g(n)=−50−15n g(n)=-50-15 n \newlineComplete the recursive formula of g(n) g(n) .\newline g(1) = \(\square\) \newline g(n) = g(n-1)+\(\square\)
  1. Find g(1)g(1): To find the recursive formula for the sequence, we need to express g(n)g(n) in terms of g(n−1)g(n-1). First, let's find the value of g(1)g(1) by substituting n=1n=1 into the given formula g(n)=−50−15ng(n)=-50-15n.\newlineCalculation: g(1)=−50−15(1)=−50−15=−65g(1) = -50 - 15(1) = -50 - 15 = -65
  2. Find g(2)g(2): Now, let's find g(2)g(2) to determine the common difference between terms. We substitute n=2n=2 into the given formula g(n)=−50−15ng(n)=-50-15n.\newlineCalculation: g(2)=−50−15(2)=−50−30=−80g(2) = -50 - 15(2) = -50 - 30 = -80
  3. Calculate common difference: The common difference dd between terms can be found by subtracting g(1)g(1) from g(2)g(2).\newlineCalculation: d=g(2)−g(1)=−80−(−65)=−80+65=−15d = g(2) - g(1) = -80 - (-65) = -80 + 65 = -15
  4. Write recursive formula: Now we can write the recursive formula. Since the common difference is −15-15, the recursive formula will be g(n)=g(n−1)−15g(n) = g(n-1) - 15.

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