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Example 12 - Find sum of first n terms and of first 5 terms - Examples

Example 12 - Chapter 9 Class 11 Sequences and Series - Part 2
Example 12 - Chapter 9 Class 11 Sequences and Series - Part 3

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Example 12 Find the sum of first n terms and the sum of first 5 terms of the geometric series 1 + 2/3 "+" 4/9 + ……… 1 + 2/3 "+" 4/9 + ……… We know that 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 Here, First term = a = 1 and common ratio = r = (2/3)/1 Now, we need to calculate sum of n terms of GP We use the formula, Sn = (a(1 − 𝑟^𝑛))/(1 − r) Putting a = 1 , r = 2/3 = 1(1 − ( 2/3)^𝑛 )/(1 − 2/3) = (1 − ( 2/3)^𝑛)/((3 − 2)/3) = (1 − ( 2/3)^𝑛)/(1/3) = 3/1 ["1 –" (2/3)^𝑛 ] = 3["1 –" (2/3)^𝑛 ] Thus, Sum of n terms = Sn = 3["1 –" (2/3)^𝑛 ] Now, we need to find sum of first 5 terms of GP Putting n = 5 in Sn S5 = 3["1 –" (2/3)^5 ] = 3 ["1 –" (2^5/3^5 )] = 3 ["1 –" (32/243)] = 3 [(243 − 32)/243] = 3 [211/243] = 211/81 Hence, sum of first five terms of GP is 211/81

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.