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If pth, qth, and rth terms of an A.P. ar...

If pth, qth, and rth terms of an A.P. are `a ,b ,c ,` respectively, then show that `a(q-r)+b(r-p)+c(p-q)=0` `(a-b)r+(b-c)p+(c-a)q=0`

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CENGAGE-PROGRESSION AND SERIES-Examples
  1. In a certain AP, 5times the 5^(th) term is equal to 8 times the 8^(th)...

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  2. Find the term of the series 25 ,22 ,3/4,20 1/2,18 1/4 which is numeric...

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  3. If pth, qth, and rth terms of an A.P. are a ,b ,c , respectively, then...

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  4. Consider two A.P. s: S1:2,7,12 ,17 , 500t e r m s a n dS1:1,8,15 ,22 ,...

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  5. If a1,a2,a3, ,an are in A.P., where ai >0 for all i , show that 1/(sqr...

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  6. If p,q and r (pneq) are terms ( not necessarily consecutive) of an A.P...

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  7. If the terms of the A.P. sqrt(a-x),sqrt(x),sqrt(a+x) are all in intege...

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  8. If (b+c-a)/a ,(c+a-b)/b ,(a+b-c)/c , are in A.P., prove that 1/a ,1/b ...

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  9. If a ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+1//(a c),...

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  10. If a,b,c are in A.P., then prove that the following are also in A.P ...

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  11. If the sum of three numbers in A.P., is 24 and their product is 440, f...

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  12. Divide 32 into four parts which are in A.P. such that the ratio of the...

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  13. The digits of a positive integer, having three digits, are in A.P. and...

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  14. If eleven A.M. s are inserted between 28 and 10, then find the number ...

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  15. Between 1 and 31, m numbers have been inserted in such a way that the ...

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  16. Find the sum of all three-digit natural numbers, which are divisible b...

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  17. Find the number of terms in the series 20 ,19 1/3,18 2/3... the sum of...

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  18. Find the degree of the expression (1+x)(1+x^6)(1+x^(11))(1+x^(101))dot

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  19. Find the sum of first 24 terms of the A.P. a1, a2, a3, , if it is kno...

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  20. If S1 is the sum of an AP of 'n' odd number of terms and S2 be the sum...

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