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If a, b, c are In A.P., then show that, ...

If a, b, c are In A.P., then show that,
`a^(2)(b+c), b^(2)(c+a), c^(2)(a+b)` are in A.P. `(ab+bc+ca != 0)`

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If a, b, c are In A.P., then show that, (1)/(b c), (1)/(c a), (1)/(a b) are in A.P.

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If a, b, c are in A.P., show that, (bc)/(a(b+c)), (ca)/(b(c+a)) and (ab)/(c(a+b)) are in H.P.

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CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 B (Short Answer Type Questions)
  1. There are n arithmetic means between 4 and 31 such that the second mea...

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  2. If a, b, c are In A.P., then show that, (a+2b-c) (2b+c-a)(c+a-b) = 4...

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  3. If a, b, c are In A.P., then show that, a^(2)(b+c), b^(2)(c+a), c^(2...

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  4. If a, b, c are In A.P., then show that, (1)/(b c), (1)/(c a), (1)/(a...

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  5. If the pth , qth and rth terms of an A.P. be P, Q and R respectively t...

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  6. If (b+c)/(a), (c+a)/(b), (a+b)/(c ) are in A.P. show that (1)/(a), (1)...

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  7. Let a(a != 0) is a fixed real number and (a-x)/(p x) = (a-y)/(qy) = (a...

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  8. If a+c = 2b and ab + cd + ad = 3bc, prove that the four numbers a, b, ...

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  9. Find the least value of n for which the sum of the series 20 + 28 + 36...

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  10. The nth term of a series in A.P. is an + b. Find the sum of the series...

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  11. Find the sum of the series 1^(2) - 2^(2) - 3^(2) - 4^(2) + 5^(2) - 6^(...

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  12. The perpendicular of a right angled triangle is 9 cm and the three sid...

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  13. If the xth term of an A.P. is (1)/(y) and its yth term is (1)/(x) then...

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  14. An A.P. consists of n terms. If the sum of its first three terms is x ...

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  15. If S be the sum of first (2n+1) terms of an A.P and the sum of terms i...

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  16. The sum of first p terms of an A.P. is (p^(2))/(n) and the sum of its ...

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  17. If the A.M. of (1)/(b-a) and (1)/(b-c) is (1)/(2(b-x)), then show that...

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  18. A farmer undertakes to pay off a debt of Rs. 2700 by monthly instalmen...

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  19. A person pays Rs.975 in monthly instalments, each instalment is less t...

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  20. If 1 paisa is saved today, 2 paise next day, 3 paise succeeding day an...

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