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The Fifth, Eight and Eleventh Terms of a Geometric Progression Are P, Q and R Respectively. Show that : Q2 = Pr. - Mathematics

Sum

The fifth, eight and eleventh terms of a geometric progression are p, q and r respectively. show that : q2 = pr.

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Solution

Let the first term of the G.P. be a and its common ratio be r.
5th term = t5 = p
⇒ ar4 = p

8th term = t8 = q
⇒ ar7 = q

11th term = t11 = r
⇒ ar10 = r

Now,
pr = ar4 x ar10 = a2 x r14 = (a x r7)2 = q2
⇒ q2 = pr

Concept: Simple Applications - Geometric Progression
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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 11 Geometric Progression
Exercise 11 (B) | Q 10 | Page 154
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