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Examine whether the following sequences ...

Examine whether the following sequences are in H.P. :
`{(1)/(c + 3d'), (1)/(c + 2d'), (1)/(c'), (1)/(c - 3d'),…}`

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The correct Answer is:
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If positive quantities a,b,c are in H.P. , then which of the following is not true ? a. b gt (a+c)/(2) b. (1)/(a-b)-(1)/(b-c) gt 0 c. ac gt b^(2) d. none of these

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If a, b, c, d are four distinct numbers in A.P. , show that 1/a + 1/d gt 1/b + 1/c gt 4/(a + d)

If a,b,c be in H.P prove that (1/a+1/b-1/c)(1/b+1/c-1/a)=4/(ac)-3/b^2

let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d)),1/( (a + d) (a +2d))],[1/(a+ d),1/( (a+ d) (a + 2d)), 1/((a+2d) (a + 3d))],[1/(a +2d), 1/((a + 2d) (a +3d)), 1/((a+3d) (a + 4d))]|

CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 E (Very Short Answer Type Questions)
  1. Examine whether the following sequences are in H.P. : {(1)/(7), (1)...

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  2. Examine whether the following sequences are in H.P. : {(1)/(a-3b), ...

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  3. Examine whether the following sequences are in H.P. : {(1)/(c + 3d'...

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  4. Find the H.P whose first and second terms are (1)/(3) are (1)/(5) resp...

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  5. If the 10th and 19th terms of a H.P. are (-(5)/(37)) and (-(5)/(64)) r...

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  6. If the pth term of a H.P. be q and the qth term be equal to p, show th...

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  7. What is the value of the H.M. between (a+b) and (a-b) ?

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  8. Insert two HM.s between (1)/(3) and (1)/(24).

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  9. Insert two H.M.s between (-6) and (3)/(13).

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  10. If the G.M. and H.M. of two numbers are 15 and 9 respectively, find th...

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  11. If the A.M. and H.M. of two numbers are 15 and 9(3)/(5) respectively, ...

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  12. If the ratio of G.M. of two numbers to their H.M. is 5 : 4, prove tha...

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  13. If a, b, c are in H.P., prove that, (a)/(b+c-a), (b)/(c+a-b), (c )/...

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  14. If a, b, c are in H.P., prove that, (1)/(bc), (1)/(ca), (1)/(ab) ar...

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  15. 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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  16. If a, b, c are in H.P., prove that, (a)/(a-b) = (a+c)/(a-c)

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

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  18. If a^(2), b^(2), c^(2) are in A.P., show that, (b+c), (c+a), (a+b) are...

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  19. If four positive numbers a, b, c and d are in A.P. then prove that abc...

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  20. Prove that, a, b,c are in A.P., G.P. or, H.P. accordingly as (a-b)/(b-...

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