Ex 9.3, 4 - The 4th term of GP is square of its second term - Geometric Progression(GP): Formulae based

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  1. Chapter 9 Class 11 Sequences and Series
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Ex 9.3,4 The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7th 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, First term = a = – 3 Also, 4th term of G.P = (2nd term of G.P.)2 i.e. a4 = (a2)2 Putting values in (1) ar4 – 1 = (ar2 – 1)2 ar3 = (ar1)2 ar3 = (ar)2 ar3 = a2 r2 𝑟^3/𝑟^2 = 𝑎^2/𝑎 𝑟^(3−2) = 𝑎^(2−1) r1 = a1 r = a Putting a = -3 r = -3 Thus, r = -3 & a = -3 Now we need to find 7th term, we use the formula an = arn – 1 Putting n = 7 , a = – 3, r = – 3 a7 = (–3) (–3)7 – 1 = (–3) (–3)6 = (-3) × 729 = – 2187 Hence, 7th term is – 2187

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