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प्रश्न
The fifth, eight and eleventh terms of a geometric progression are p, q and r respectively. Show that : q2 = pr.
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उत्तर
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 × ar10
= a2 × r14
= (a × r7)2
= q2
`=>` q2 = pr
संबंधित प्रश्न
Find, which of the following sequence from a G.P. :
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If a, b and c are in A.P. and also in G.P., show that : a = b = c.
Find the sum of G.P. :
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Q 7
Q 8
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Find a G.P. for which the sum of first two terms is – 4 and the fifth term is 4 times the third term.
