Subjects algebra

Sequence Formula

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1. **State the problem:** We are given the sequence $$79, 71, 63, 55, \ldots$$ and asked to find the explicit formula for the sequence where the first term corresponds to $$h(1)$$. 2. **Check Emeka's formula:** $$h(n) = 79 - 8(n-1)$$. - Substitute $$n=1$$: $$h(1) = 79 - 8(1-1) = 79 - 0 = 79$$ which matches the first term. - Substitute $$n=2$$: $$h(2) = 79 - 8(2-1) = 79 - 8 = 71$$ which matches the second term. 3. **Check Maricel's formula:** $$h(n) = 87 - 8n$$. - Substitute $$n=1$$: $$h(1) = 87 - 8(1) = 87 - 8 = 79$$ which matches the first term. - Substitute $$n=2$$: $$h(2) = 87 - 8(2) = 87 - 16 = 71$$ which matches the second term. 4. **Check further terms to confirm:** - For Emeka's formula at $$n=3$$: $$h(3) = 79 - 8(3-1) = 79 - 16 = 63$$ matches the third term. - For Maricel's formula at $$n=3$$: $$h(3) = 87 - 8(3) = 87 - 24 = 63$$ matches the third term. 5. **Conclusion:** Both formulas generate the same sequence for all $$n$$ because: $$79 - 8(n-1) = 79 - 8n + 8 = 87 - 8n$$. **Answer:** Both Emeka and Maricel are correct.