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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-b)r+(b-c)p+(c-a)q=0`

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. Find the sum of the following series: 1/2+1/(3^2)+1/(2^3)+1/(3^4)+1/(...

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  2. Consider two A.P.: S2:2,7,12 ,17 , 500 terms a n dS1:1,8,15 ,22 , 300 ...

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

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  4. The sum of the first four terms of an A.P. is 56. The sum of the last ...

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  5. Given two A.P. 2,5,8,11...... T(60) and 3,5,7,9,......... T(50)dot Th...

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  6. In a certain A.P., 5 times the 5th term is equal to 8 times the 8th ...

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

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  8. How many terms are there in the A.P. 3, 7, 11, ... 407?

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  9. If a ,b ,c ,d ,e are in A.P., the find the value of a-4b+6c-4d+edot

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

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  12. Find the degree of the expression (1+x)(1+x^6)(1+x^(11))........(1+x^(...

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  13. In an A.P. of 99 terms, the sum of all the odd-numbered terms is 2550....

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

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  15. Show (m+n)th and (m-n)t h terms of an A.P. is equal to twice the mth ...

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  16. If the sum of three consecutive numbers in A.P., is 24 and their pr...

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  17. Prove that the sum of n number of terms of two different A.P. s can be...

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  18. In an A.P. if S1=T1+T2+T3+.....+Tn (n is odd)S2=T2+T4+T6+.........+T(n...

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  19. If the sum of the series 2, 5, 8, 11, ... is 60100, then find the valu...

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

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