A family of chemical compounds are made up of carbon, hydrogen and oxygen atoms. The number of carbo

Question

A family of chemical compounds are made up of carbon, hydrogen and oxygen atoms. The number of carbon, hydrogen and oxygen atoms of each of the first four members in the family are shown in the following table. Complete the table: Find a formula that represents the relationship between the number of carbon atoms, $C_n$ and the number of hydrogen atoms, $H_n$ of the $n^{th}$ member in the family. Suppose the $m^{th}$ member of the family has $50$ hydrogen atoms, find the value of $m$. Hence find the number of carbon atoms, $C_m$ and the number of oxygen atoms, $O_m$ that this member has.

Accepted Answer

(i) Member 5: $C_5=5$, $H_5=10$, $O_5=2$ Member 6: $C_6=6$, $H_6=12$, $O_6=2$ Member $n$: $C_n=n$, $H_n=2n$, $O_n=2$ (ii) $H_n=2C_n$ (iii) $m=25$, $C_m=25$, $O_m=2$

Number Patterns

Number Patterns

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