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Ex 9.3, 19 - Find sum of products of 2, 4, 8, 16, 32 - Geometric Progression(GP): Formulae based

  1. Chapter 9 Class 11 Sequences and Series
  2. Serial order wise
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Ex 9.3, 19 Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, 1/2 1st sequence is 2, 4, 8, 16, 32 2nd sequence is 128, 32, 8, 2, 1/2 Let P = Sum of product of corresponding terms of 1st & 2nd sequences. P = 2 × 128 + 4 × 32 + 8 × 8 + 16 × 2 + 32 × 1/2 P = 256 + 128 + 64 + 32 + 16 P = 256 + 128 + 64 + 32 + 16 Now, in 256 , 128 , 64 , 32 ,16 128/256 = 1/2 & 64/128 = 1/2 Thus, (𝑆𝑒𝑐𝑜𝑛𝑑 𝑡𝑒𝑟𝑚)/(𝐹𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚) = (𝑇ℎ𝑖𝑟𝑑 𝑡𝑒𝑟𝑚)/(𝑆𝑒𝑐𝑜𝑛𝑑 𝑡𝑒𝑟𝑚) i.e. common ratio is same Thus, it is a G.P Here, First term, a = 256 & common ratio r = 128/256 & n = 5 We need to find sum of these terms We need to find sum of these terms Sn = (a(1 − 𝑟^𝑛))/(1 − 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 Putting n = 5 , a = 256 , r = 1/2 S5 = (256[1 − (1/2)^5])/(1 − 1/2) = (256[1−(1/32)])/(1/2) = 256[1−(1/32)] × 2 = 256((32 − 1)/32) × 2 = 256((32 − 1)/32) × 2 = (256 × 31 × 2)/32 = 16 × 31 = 496 Hence the sum of products of corresponding terms in sequences is 496

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