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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
Fourth and seventh terms of a G.P. are `1/18` and `-1/486` respectively. Find the G.P.
If the first and the third terms of a G.P. are 2 and 8 respectively, find its second term.
If a, b and c are in G.P., prove that : log a, log b and log c are in A.P.
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. :
0.3 + 0.03 + 0.003 + 0.0003 + ........... to 8 items.
Find the sum of G.P. :
`1 - 1/3 + 1/3^2 - 1/3^3 + .........` to n terms.
Q 3.1
Q 3.2
Q 3.3
Q 7
