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

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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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Sum of the first p, q and r terms of an A.P are a, b and c, respectively.Prove that a/p(q-r)+b/q(r-p)+c/r(p-q)=0

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RD SHARMA ENGLISH-ARITHMETIC PROGRESSIONS-All Questions
  1. How many terms are there in the sequence 3,6,9, 12 ,....... 111 ?

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  2. Is 184 a term of the sequence 3,7,11, ... ?

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

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

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  5. Show that the sum of (m+n)^(t h)a n d\ (m-n)^(t h) term of an A.P. is ...

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  6. If m times the m^(t h) term of an A.P. is equal to n times its n^(t h)...

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  7. If the p^(t h) term of an A.P. is q and the q^(t h) term is p , prove ...

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  8. If the mth term of an A.P. be 1//n and nth term be 1//m then show that...

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  9. Determine the number of terms in the terms in the A.P. 3,7,11…407. ...

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  10. How many numbers of two digits are divisible by 7?

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  11. Show that there is no A.P. which consists of only distinct prime nu...

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  12. In the arithmetic progressions 2,5,8,… upto 50 terms and 3,5,7,9… upto...

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  13. Find: 10 t h term of the A.P. 1,4,7,10..

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  14. Find: nth term of the A.P. 13,8,3,-2,…

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  15. Find: 18th term of the A.P. sqrt(2),\ 3sqrt(2),\ 5sqrt(2) ddot

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  16. Evaluate (sqrt(3)-sqrt(2))^6+(sqrt(3)+sqrt(2))^6dot

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  17. If the sequence an is A.P., show that a(m+n)+a(m-n)=2amdot\

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  18. Which term of the A.P. 3,8,13… is 248?

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  19. Which term of the A.P. 84,80,76… is 0?

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  20. Which term of the A.P. 4,9,14… is 254?

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