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Question
While studying her family’s history. Shikha discovers records of ancestors 12 generations back. She wonders how many ancestors she has had in the past 12 generations. She starts to make a diagram to help her figure this out. The diagram soon becomes very complex.
- Make a table and a graph showing the number of ancestors in each of the 12 generations.
- Write an equation for the number of ancestors in a given generation n.
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Solution
a. On the basis of given diagram, we can make a table that shows the number of ancestors in each of the 12 generations.
| Generations | Ancestors |
| 1st | 2 |
| 2nd | 22 |
| 3rd | 23 |
 |
 |
| 12th | 212 |
Hence, we can also make a graph that shows the relation between generation and ancestor.
b) On the basis of generation-ancestor graph, the number of ancestors in n generations will 2n.
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