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Ex 9.3, 7 - Find sum to 20 terms in 0.15, 0.015, 0.0015 - Ex 9.3

  1. Chapter 9 Class 11 Sequences and Series
  2. Serial order wise
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Ex 9.3,7 Find the sum to 20 terms in the geometric progression 0.15, 0.015, 0.0015 โ€ฆ 0.15, 0.015, 0.0015 โ€ฆ We know that Sn = (a(1 โˆ’ ๐‘Ÿ^๐‘›))/(1 โˆ’ r) where Sn = sum of n terms of GP n is the number of terms a is the first term r is the common ratio First term a = 0.15 , Common ratio r = 0.015/0.15 ` = 15/1000 ร— 100/15 = 1/10 We know that Sum of n term = (๐‘Ž(1 โˆ’ ๐‘Ÿ^๐‘›))/(1 โˆ’ ๐‘Ÿ) We need to find sum of 20 terms. S20 = (๐‘Ž(1 โˆ’ ๐‘Ÿ^20))/(1 โˆ’ ๐‘Ÿ) We need to find sum of 20 terms, we use the formula Sn = (a(1 โˆ’ ๐‘Ÿ^๐‘›))/(1 โˆ’ r) Putting a = 0.15, r = 0.1,n=20 S20 = (0.15(1 โˆ’(0.1)20))/(1 โˆ’ 0.1) S20 =(0.15(1 โˆ’(0.1)20))/0.9 S20 = 1/6[ 1 โ€“ (0.1)20] Hence, sum of 20 terms of GP is 1/6[ 1 โ€“ (0.1)20]

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