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Example 16 - A person has 2 parents, 4 grandparents, 8 great - Examples

  1. Chapter 9 Class 11 Sequences and Series
  2. Serial order wise
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Example 16, A person has 2 parents, 4 grandparents, 8 great grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own. The number of ancestors are 2,4,8,16, โ€ฆ It is a G.P. since, 4/2 = 2 8/4 = 2 โˆด Common ratio = 2 First term = a = 2 & number of generations (n) = 10 We have to find the number of his ancestors during the ten generations preceding his own, i.e. S10 As r > 1 Sum of n terms in GP = (a(๐‘Ÿ^๐‘› โˆ’ 1))/(r โˆ’ 1) i.e. Sn = (a(๐‘Ÿ^๐‘› โˆ’ 1))/(r โˆ’ 1) Putting values of a=2, r=2, & n=10 S10 = (2(210 โˆ’ 1))/(2 โˆ’ 1) S10 = (2(210 โˆ’ 1))/1 S10 = (210 + 1 โ€“ 2) S10 = 211 โ€“ 2 S10 = 2048 โ€“ 2 S10 = 2046 Hence, the number of ancestors preceding the person is 2046.

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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