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We know that, if a1, a2, ..., an are in...

We know that, if `a_1, a_2, ..., a_n` are in H.P. then `1/a_1,1/a_2,.....,1/a_n` are in A.P. and vice versa. If `a_1, a_2, ..., a_n` are in A.P. with common difference d, then for any `b (>0)`, the numbers `b^(a_1),b^(a_2),b^9a_3),........,b^(a_n)` are in G.P. with common ratio `b^d`. If `a_1, a_2, ..., a_n` are positive and in G.P. with common ration, then for any base `b (b> 0), log_b a_1 , log_b a_2,...., log_b a_n` are in A.P. with common difference logor.If `x, y, z` are respectively the pth, qth and the rth terms of an A.P., as well as of a G.P., then `x^(z-x),z^(x-y)` is equal to

Answer

Step by step text solution for We know that, if a_1, a_2, ..., a_n are in H.P. then 1/a_1,1/a_2,.....,1/a_n are in A.P. and vice versa. If a_1, a_2, ..., a_n are in A.P. with common difference d, then for any b (>0), the numbers b^(a_1),b^(a_2),b^9a_3),........,b^(a_n) are in G.P. with common ratio b^d. If a_1, a_2, ..., a_n are positive and in G.P. with common ration, then for any base b (b> 0), log_b a_1 , log_b a_2,...., log_b a_n are in A.P. with common difference logor.If x, y, z are respectively the pth, qth and the rth terms of an A.P., as well as of a G.P., then x^(z-x),z^(x-y) is equal to by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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Knowledge Check

  • If a_1,a_2,…………..a_n are in AP with common difference d ne 0 then find (sin d) [sec a_1 sec a_2+ sec a_2 sec a_3+…….+sec a_(n-1) sec a_n]

    A
    `cot a_n- cot a_1`
    B
    `cot a_1-cot a_n`
    C
    `tan a_n- tan a_1`
    D
    `tan a_n- tan a_(n-1)`

  • If a_1,a_2,…,a_n are in AP with common difference dne0 , then (sin d) [sec a_1 sec a_2 + sec a_3 +...+sec a_(n-1) sec a_n ] is equal to

    A
    `cot a_n-cota_1`
    B
    `cot a_1-cota_n`
    C
    `tana_n-tana_1`
    D
    `tana_n-tana_(n-1)`

  • If a_1,a_2,…,a_n are in AP with common difference d, then the sum of the series sin d(cosec a_1 cosec a_2 +cosec a_2 cosec a_3 +…+cosec a_(n-1) cosec a_n ) is

    A
    sec `a_1`- sec `a_n`
    B
    cot `a_1`- cot `a_n`
    C
    tan `a_1`- tan `a_n`
    D
    cosec `a_1`- cosec `a_n`

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