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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. :
`1/8, 1/24, 1/72, 1/216, ................`
Find, which of the following sequence from a G.P. :
9, 12, 16, 24, ................
Which term of the G.P.:
`-10, 5/sqrt(3), -5/6,....` is `-5/72`?
The fourth term, the seventh term and the last term of a geometric progression are 10, 80 and 2560 respectively. Find its first term, common ratio and number of terms.
Q 5
If a, b and c are in G.P., prove that : log a, log b and log c are in A.P.
Find the sum of G.P. :
0.3 + 0.03 + 0.003 + 0.0003 + ........... to 8 items.
Find the sum of G.P. :
`sqrt(3) + 1/sqrt(3) + 1/(3sqrt(3)) + ..........` to n terms.
Q 3.2
The first term of a G.P. is –3 and the square of the second term is equal to its 4th term. Find its 7th term.
