Madhav went to a wedding along with his parents. He met many relatives there. But he didn't know everyone. He met his mother's grandfather, but found that her grandmother is not alive. He also found that her Dadi's mother (grandmother's mother) is still alive, and is more than a hundred years old.
Madhav got confused. He couldn't imagine his mother's grandmother's mother! So, Madhav's mother made a family tree for him —

Madhav's mother helped him understand her family with the help of this drawing. You can also find out about your older generations using such a family tree.

Answer these questions:
(1) How many grand parents in all does Shobna have?
(2) How many great, great grand parents in all does Madhav have?
(3) How many elders will be in the VII generation of his family?
(4) If he takes his family tree forward in which generation will he find 128 elders?

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Solution

(1)
Shobna has 4 grandparents.

(2)
Madhav has 8 great, great grandparents in all.

(3)
Number of members in III generation of Madhav's family = 2
Number of members in IV generation of Madhav's family = 2 × 2
= 4
Number of members in V generation of Madhav's family = 4 × 2
= 8
Number of members in VI generation of Madhav's family = 8 × 2
= 16
And number of members in VII generation of Madhav's family = 16 × 2
= 32
Thus, there would be 32 elders in the VII generation of Madhav's family.

(4)
Number of members in VII generation of Madhav's family = 32
Number of members in VIII generation of Madhav's family = 32 × 2 = 64
Number of members in IX generation of Madhav's family = 64 × 2 = 128

Thus, in the IX generation, number of elders in Madhav's family will be 128.

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