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If the sum of n terms of an A.P. is (p n...

If the sum of n terms of an A.P. is `(p n+q n^2)`, where p and q are constants, find the common difference.

Text Solution

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Given `S_n=Pn+Qn^2`
`:. T_n=S_n-S_(n-1)`
`=Pn+Qn^2-[P(n-1)+Q(n-1)^2]`
`=P-Q+2nQ`
...
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NCERT-SEQUENCES AND SERIES-EXERCISE 9.2
  1. Sum of the first p, q and r terms of an A.P are a, b and c, respectiv...

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  2. Insert five numbers between 8 and 26 such that the resulting sequence...

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  3. A mail starts repaying a loan as first instalment of Rs. 100. If he i...

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  4. The difference between any two consecutive interior angles of a polyg...

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

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  6. If the sum of first p terms of an A.P. is equal to the sum of the fir...

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  7. If the sum of n terms of an A.P. is 3n^(2)+5n and its mth term is 164,...

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  8. The ratio of the sum of m and n terms of an A.P. is m^(2) :n^(2). Show...

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  9. If (a^n+b^n)/(a^(n-1)+b^(n-1))is the A.M. between a and b, then find t...

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  10. If the sum of n terms of an A.P. is (p n+q n^2), where p and q are co...

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  11. The sums of n terms of two arithmetic progressions are in the ratio 5...

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  12. If the sum of a certain number of terms of the A.P. 25, 22, 19.... is...

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  13. Find the sum to n terms of the A.P., whose k^(t h)term is 5k + 1.

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  14. How many terms of the A.P. 6, -(11)/2,-5,...........are needed to gi...

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  15. In an A.P., if p^(t h)term is 1/qand q^(t h)term is 1/p, prove that t...

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  16. Find the sum of all natural numbers lying between 100 and 1000, which...

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

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  18. Find the sum of odd integers from 1 to 2001.

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