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Let the sum of n, 2n, 3n terms of an A.P...

Let the sum of n, 2n, 3n terms of an A.P. be `S_1, S_2 and S_3` , respectively, show that `S_3 =3(S_2-S_1)`

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If the sums of n, 2n and 3n terms of an A.P. be S_(1), S_(2), S_(3) respectively, then show that, S_(3) = 3(S_(2) - S_(1)) .

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If the first term, common ratio and the sum of first n terms of a G.P. be a, r and S_(n) respectively, find the value of S_(1) + S_(2) + S_(3) +….+S_(n) .

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If S_1,S_2 and S_3 be respectively the sum of n, 2n and 3n terms of a G.P., prove that S_1(S_3-S_2)=((S_2)-(S_1))^2

NCERT BANGLISH-SEQUENCES AND SERIES-Miscellaneous Exercise On Chapter 9
  1. Show that the sum of (m + n)^(th) and (m – n)^(th) terms of an A.P. ...

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

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  3. Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3 , respectiv...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. 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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