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If the nth term of a G.P. be p, then sho...

If the nth term of a G.P. be p, then show that the product of its first (2n-1) terms is `p^(2n-1)`.

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If the sum of first n terms of G.P. is S and the sum of its first 2n terms is 5S, then show that the sum of its first 3n terms is 21S.

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The nth term of an A.P. is p and the sum of its first n terms is q. Prove that its first term is (1)/(n)(2q-p n) .

The sum of first p terms of an A.P. is (p^(2))/(n) and the sum of its first q(!= p) terms is (q^(2))/(n) . Show that the sum of its first n terms will be n.

There are m A.P. Whose common differences are 1,2,3,.. M respectively, the first term of each being unity. Show that the sum of their nth terms is (m)/(2)(mn -m+n+1) .

The second term of a G.P. is b and the common ratio is r. If the product of the first three terms of this G.P. is 64, find b.

If the P^(th) and q^(th) terms of an A.Pare a and b respectively,then show that the sum of first (p+q) terms of thath A.P is 1/2(p+q) (a+b+(a-b)/(p-q))

CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 C (Very Short Answer Type Questions)
  1. If 5, x, y, z, 405, are the first five terms of a G.P., find the value...

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  2. The second term of a G.P. is b and the common ratio is r. If the produ...

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  3. Find the 10th and pth terms of the G.P. {2, 6, 18, 54,…}

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  4. Find the 9th and qth terms of the G.P. {4, -8, 16, -32,…}

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  5. Find the 14th and nth terms of the G.P. {sqrt(5), 1, (1)/(sqrt(5)), ...

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  6. If the 3rd term of a G.P. is the square of the first term and its fift...

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  7. If the (p+q)th term of a G.P. is a and (p-q)th term is b, determine it...

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  8. If the nth term of a G.P. be p, then show that the product of its firs...

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  9. Which term of the G.P. {sqrt(2), sqrt(6), 3sqrt(2), 3sqrt(6),…} is 243...

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  10. Is 256 a term of the G.P. {3, 6, 12, 24,…} ?

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  11. Fill in the gaps (indicated by) in each of the following G.P.'s. (11...

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  12. Fill in the gaps (indicated by) in each of the following G.P.'s. -1,...

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  13. Fill in the gaps (indicated by) in each of the following G.P.'s. 0.1...

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  14. Find r if (i) 3r+1, 7r, 10r+8 are in G.P., (ii) 2r, 4r+1, 6r+2 are in ...

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  15. Insert four geometric means between (7)/(4) and 56.

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  16. If three unequal positive numbers a, b, c are in G.P. then show that, ...

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  17. Three different numbers a, b, c are both in A.P. G.P. - is it possible...

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