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If a, b, c be the pth, qth and rth term ...

If a, b, c be the pth, qth and rth term of both an A.P. and G.P., then show that - `a^(b-c).b^(c-a).c^(a-b)=1`.

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If pth, qth and rth term of an A.P. be a,b,c then prove that. a(q-r)+b(r-p)+c(p-q)=0

If pth, qth and rth term of an A.P. are in G.P., then show that common ratio of the G.P. is (q-r)/(p-q) .

If pth, qth and rth term of a G.P. are in G.P. then prove that p, q, r are in A.P.

If pth, qth and rth term of an A.P. are in A.P., show that p, q, r also are in A.P.

The pth, qth and rth term of a G.P. are x, y, z respectively, then prove that- x^(q-r).y^(r-p).z^(p-q)=1 .

If a,b,c are in G.P then show that a(b^2-c^2)=c(a^2-b^2)

If a,b,c,d are in G.P then show that (b-c)^2+(c-a)^2+(d-b)^2=(a-d)^2 .

If a,b,c are in G.P then show that a(b^2+c^2)=c(a^2+b^2)

If a, b, c are in A.P. and also in GP., show that a = b = c.

If the sums of an A.P. upto pth, qth and rth terms are a, b and c respectively, prove that- a/p(q-r)+b/q(r-p)+c/r(p-q)=0 .

KALYANI PUBLICATION-PROGRESSION-EXERCISE
  1. If pth, qth and rth term of a G.P. are in G.P. then prove that p, q, r...

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  2. If pth, qth and rth term of an A.P. are in G.P., then show that common...

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  3. If a, b, c be the pth, qth and rth term of both an A.P. and G.P., then...

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  4. If a, b, c, d are in G.P., show that each of the following three term ...

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  5. If a,b,c,d are in G.P show that each of the following three term are a...

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  6. If a,b,c,d are in G.P show that each of the following three term are a...

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  7. If a,b,c,d are in G.P show that each of the following three term are a...

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  8. If a, b, c, d are in G.P., show that each of the following three term ...

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  9. If a,b,c,d are in G.P show that each of the following three term are a...

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  10. If a,b,c,d are in G.P show that each of the following three term are a...

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  11. Insert three G.M.’s between 1 and 256.

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  12. Insert five G.M.'s between 8 and 1/8.

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  13. Insert five G.M.’s between 3 and 192.

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  14. Insert four G.M.'s between 7/4 and 56.

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  15. If 1/2 , x, y, z, 128 are in G.P., then find x,y,z,

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  16. Inserting three G.M.'s between 1/9 and 9 verify that their product is ...

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  17. The A.M. and G.M. of two positive numbers are 25 and 24 respectively. ...

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  18. The A.M. and G.M. of two positive numbers are 15 and 9 respectively...

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  19. The A.M. of two integral numbers exceeds their G.M. by 2 and the ratio...

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  20. The sum of two positive numbers is 13 and their G.M. is 6. Find them.

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