Examples

Chapter 8 Class 11 Sequences and Series
Serial order wise

### Transcript

Example 6, In a G.P., the 3rd term is 24 and the 6th term is 192. Find the 10th term. We know that an = arn – 1 where an = nth term of GP n is the number of terms a is the first term r is the common ratio Here, 3rd term is 24 i.e. a3 = 24 Putting an = 24, n = 3 in an formula 24 = a 𝑟^(3−1) 24 = ar2 ar2 = 24 Similarly, Given 6th term is 192 i.e. a6 = 192 Putting an = 192, n = 6 in an formula 192 = a 𝑟^(6−1) 192 = ar5 ar5 = 192 Now, our equations are ar2 = 24 …(1) & ar5 = 192 …(2) Dividing (2) by (1), ar5/ar2 = 192/24 𝑟5/𝑟2 = 8 𝑟5/𝑟2 = 8 r5 – 2 = 8 r3 = 8 r3 = 2 × 2 × 2 r3 = (2)3 r = 2. putting r in (1) ar2 = 24 a(2)2 = 24 a (4) = 24 a = 24/4 a = 6 Thus, a = 6 & r = 2 Now we need to find 10th term, we use the formula an = arn – 1 Putting n = 10 , a = 6, r = 2 a10 = ar10 – 1 = (6)(2)10 – 1 = 6 (2)9 = 3072 Hence, 10th term of GP is 3072

#### 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.
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