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Find the AP in which the ratio of the su...

Find the AP in which the ratio of the sum to `n` terms to the sum of succeding `n` terms is independent of `n`.

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In an A.P. with first term 'a' and the common difference d(a, d!= 0) , the ratio 'rho' of the sum of the first n terms to sum of n terms succedding them does not depend on n . Then the ratio (a)/(d) and the ratio 'rho' , respectively are

In an A.P. with first term 'a' and the common difference d (a, d!=0), the ratio 'rho' of the sum of the first n terms to sum of n terms succeeding them does not depend on n. Then the ratio a/d and the ratio, 'rho' ,respectively are

if nth term of an AP is 3n+2 then find the sum n terms.

If the ratio of the sum of n terms of two AP'sis 2n:(n+1), then ratio of their 8th term is

If the sum of m terms of an AP is the same as the sum of its n terms , show that the sum of its (m+n) terms is zero .

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A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
  1. The number of terms in an AP is even. The sum of the odd terms is 24 w...

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  2. The ratio of the sums of n terms of two Aps is (3n-13) : (5n+21). Find...

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  3. Find the AP in which the ratio of the sum to n terms to the sum of suc...

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  4. If x,2x+2,3x+3 are the first three terms of a GP, find the fifth term ...

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  5. In a GP, t4=27 and t7=729. Find t(11) where tn denotes the nth term.

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  6. In a GP, t4=27 and t7=729. Find t(11) where tn denotes the nth term.

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  7. In a GP, t(p+q)=a and t(p-q)=b. Prove that tp=sqrt(ab).

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  8. If the pth, qth and rth terms of a G.P. are a,b and c, respectively. ...

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  9. If a be the first term, b be the nth term and P be the product of n te...

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  10. If a,b,c are in GP, prove that (a^2-b^2)(b^2+c^2)=(b^2-c^2)(a^2+b^2).

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  11. If a, b, c, d are in G.P., then prove that: (b-c)^(2)+(c-a)^(2)+(d-b...

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  12. If a,b,c,d are in GP then prove that a+b,b+c,c+d are in GP.

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  13. If a,b,c,d are in GP then prove that a(b-c)^3=d(a-b)^3.

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  14. If a,b,c,d are in GP then prove that ax^3+bx^2+cx+d has a factor ax^2+...

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  15. Let a1,a2,a3,.....,an be in GP whose common ratio is r. Show that sum(...

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  16. Does there exist a GP containing 27,8 and 12 as threee of its terms ? ...

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  17. Prove that no GP can have three of its terms (not necessarily consecut...

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  18. The product of three numbers in GP is 216 and their sum is 19. Find th...

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  19. Divide 63 into three parts that are in GP and the product of the first...

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  20. The first term of a GP is unity. For what value of the common ratio of...

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