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If a(1), a(2), ……., a(n) are in A.P. wit...

If `a_(1), a_(2), ……., a_(n)` are in A.P. with common differece `d != 0`, then `(sin d) [sec a_(1) sec a_(2) + sec a_(2) sec a_(3) + .... + sec a_(n - 1) sec a_(n)]` is equal to

A

a. `cot a_(n) - cot a_(1)`

B

b. `cot a_(1) - cot a_(n)`

C

c. `tan a_(n) - tan a_(1)`

D

d. `tan a_(n) - tan a_(n - 1)`

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The correct Answer is:
D
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NEW JOYTHI PUBLICATION-SEQUENCES AND SERIES -QUESTIONS FROM COMPETITIVE EXAMS
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  2. If a(1), a(2) …… a(n) = n a(n - 1), for all positive integer n gt= 2, ...

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  3. If a(1), a(2), ……., a(n) are in A.P. with common differece d != 0, the...

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  4. Let a be a positive number such that the arithmetic mean of a and 2 e...

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  5. If the sum to first n terms of the A.P. 2, 4, 6, …. is 240, then the v...

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  6. The value of 1/(sqrt(10) - sqrt(9)) - 1/(sqrt(11) - sqrt(10)) + 1/(sqr...

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  7. An A.P. consists of 23 terms. If the sum of the three terms Is the mid...

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  8. If a(1), a(2), a(3), ......... , are in A.P. with common difference 5 ...

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  9. The sum of all two digit natural numbers which leave a remainder 5 whe...

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  10. If the 9^(th) term of A.P. is zero, then the ratio of 29^(th) term to ...

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  11. Let S(1), S(2), ...... S(101) be consecutive terms of A.P. If 1/(S(1)S...

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  12. If a(1), a(2), a(3), ……. , a(n) are in A.P. and a(1) = 0, then the val...

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  13. The value of 1^(2) - 2^(2) + 3^(2) - 4^(2) + ….. + 11^(2) is equal to

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  14. Let s(n) denote the sum of first n terms of an A.P. and S(2n) = 3S(n)....

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  15. The first four terms of an A.P. are a, 9, 3a - b, 3a + b. The 2011^(th...

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  16. If log(e)5,log(e)(5^(x) - 1) and log(e)(5^(x) - 11/5) are in A.P., th...

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  17. The sum to n terms of the series 4/3 + 10/9 + 28/27 + ……. is

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  18. If sum(k = 1)^(n) k (k + 1)(k - 1) = pn^(4) + qn^(3) + tn^(2) + sn whe...

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  19. In an A.P., the first term is 2 and the sum of first five terms is 5. ...

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  20. If a, b, c, d are in G.P., then (a + b + c + d)^(2) is equal to

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