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Example 11, 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, … It is a G.P. since, 4/2 = 2 8/4 = 2 ∴ 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(𝑟^𝑛 − 1))/(r − 1) i.e. Sn = (a(𝑟^𝑛 − 1))/(r − 1) Putting values of a=2, r=2, & n=10 S10 = (2(210 − 1))/(2 − 1) S10 = (2(210 − 1))/1 S10 = (210 + 1 – 2) S10 = 211 – 2 S10 = 2048 – 2 S10 = 2046 Hence, the number of ancestors preceding the person is 2046.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.