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If the sum of n terms of an A.P. is nP+...

If the sum of n terms of an A.P. is `nP+1/2n(n-1)Q` , where P and Q are constants, find the common difference.

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The correct Answer is:
the common differnce is given by `d = a_(2) - a_1 = (P+Q) - P = Q`
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NCERT TAMIL-SEQUENCES AND SERIES-Miscellaneous Exercise On Chapter 9
  1. If the sum of n terms of an A.P. is nP+1/2n(n-1)Q , where P and Q are...

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  2. Show that the sum of (m+n)^(th)and(m-n)^(th) term of an A.P is equal t...

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

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  4. The sum of first n, 2n and 3n terms of an A.P. are S(1), S(2), S(3) re...

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  5. Find the sum of all numbers between 200 and 400 which are divisible by...

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  6. Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

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  7. Find the sum of all two digit numbers which when divided by 4, yields ...

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  8. If f is a function satisfying f (x +y) = f(x) f(y) for all x, y in N ...

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  9. The sum of some terms of G.P. is 315 whose first term and the common r...

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  10. The first term of a G.P. is 1. The sum of the third term and fifth ter...

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  11. The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from t...

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  12. A G.P. consists of an even number of terms. If the sum of all the term...

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

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  14. If (a+bx)/(a-bx)=(b-cx)/(b-cx)=(c+dx)/(c-dx)( x ne 0) then show that ...

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  15. Let S be the sum, P the product and R the sum of reciprocals of n term...

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  16. The p^(th), q^(th) and r^(th) terms of an A.P. are a, b, c, respectiv...

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

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  18. If a, b, c, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n +...

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  19. If a and b are the roots of x^2 – 3x + p = 0 and c, d are roots of x^...

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  20. The ratio of the A.M. and G.M. of two positive numbers a and b, is m :...

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  21. If a, b, c are in A.P., b, c, d are in G.P. and 1/c,1/d,1/e are in A.P...

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