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If a, b, c are in A.P., then prove that ...

If a, b, c are in A.P., then prove that :
`(a-c)^2 =4(b^2 -ac)`.

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MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. Each term of an A.P. is doubled. Is the resulting sequence also an A.P...

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  2. In an A.P., the mth term is 1/n and the nth term is 1/m, find the (mn)...

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  3. If a, b, c are in A.P., then prove that : (a-c)^2 =4(b^2 -ac).

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  4. Show that the sequence : log a, log (ab), log (ab^2), log (ab^3),........

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  5. How many number of two digits are divisible by 7 ?

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  6. If Sn denotes the sum of n terms of an A.P. whose first term is a, and...

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  7. If S(1),S(2),S(3),"....",S(p) are the sums of n terms of p AP's whose ...

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  8. If the sum of m terms of an AP is equal to the sum of either the next ...

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  9. If the sum of first p terms of an A.P. is equal to the sum of the firs...

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  10. The first term of an A.P. is a, the second term is b and last term is ...

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  11. Find the sum of all numbers in the first 1000 integers, which are neit...

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  12. A man gets an appointment with two options Either he can accept ₹ 45 p...

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  13. A farmer, buys a used tractor for Rs.. 12000. He pays Rs.6000 cash and...

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  14. Shamshad Ali buys a scooter for Rs 22000 He pays Rs. 4000 cash And ag...

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  15. Two cars start together in the same direction at the same place.The fi...

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  16. The ages of the students of a class form an A.P. whose common differen...

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  17. If b^2+c^2, c^2+a^2, a^2+b^2 are in A.P. prove that : 1/(b + c), 1/(c...

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  18. If a^(-1),b^(-1),c^(-1),d^(-1) are in A.P., then show that : b=(2ac)/(...

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  19. If a(1)=1, a(2)=5 find the common difference and 5th term of A.P

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  20. If the A.M. between pth and qth terms of an A.P. be equal to the A.M. ...

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