If p, q, r are in A.P., q, r, s are in G...

If p, q, r are in A.P., q, r, s are in G.P. and r, s, t are in H.P., prove that p, r, t are in G.P.

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CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 E (Very Short Answer Type Questions)

What is the value of the H.M. between (a+b) and (a-b) ?
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Insert two HM.s between (1)/(3) and (1)/(24).
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Insert two H.M.s between (-6) and (3)/(13).
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If the G.M. and H.M. of two numbers are 15 and 9 respectively, find th...
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If the A.M. and H.M. of two numbers are 15 and 9(3)/(5) respectively, ...
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If the ratio of G.M. of two numbers to their H.M. is 5 : 4, prove tha...
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If a, b, c are in H.P., prove that, (a)/(b+c-a), (b)/(c+a-b), (c )/...
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If a, b, c are in H.P., prove that, (1)/(bc), (1)/(ca), (1)/(ab) ar...
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If a, b, c are in H.P., prove that, a(b+c), b(c+a), c(a+b) are in A...
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If a, b, c are in H.P., prove that, (a)/(a-b) = (a+c)/(a-c)
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If a, b, c are in A.P., show that, (bc)/(a(b+c)), (ca)/(b(c+a)) and (a...
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If a^(2), b^(2), c^(2) are in A.P., show that, (b+c), (c+a), (a+b) are...
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If four positive numbers a, b, c and d are in A.P. then prove that abc...
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Prove that, a, b,c are in A.P., G.P. or, H.P. accordingly as (a-b)/(b-...
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If a^(x) = b^(y) = c^(z) and a, b, c, are in G.P., prove that x, y, z ...
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If p, q, r are in A.P., q, r, s are in G.P. and r, s, t are in H.P., p...
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If y is the H.M. between x and z, prove that, (1)/(y-x) + (1)/(y-z) ...
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The harmonic mean of two numbers is 4, their arithmetic mean 'A' and t...
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If the p-th, q-th and the r-th terms of a H.P. be x, y, z respectively...
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A man travels a certain distance with a uniform speed of 5 km/h ad ret...
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