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If s(1), s(2), s(3)…..s(p) are the sums ...

If `s_(1), s_(2), s_(3)…..s_(p)` are the sums of n terms of 'p' A.P's whose first terms are 1,2,3…p and common differences are 1,3,5… `(2p-1)` respectively then `s_(1) + s_(2) + s_(3) + …+ s_(p)`=

A

`pn (p n+1)`

B

`(p n)/(2) (pn +1)`

C

`p n ((p n)/(2) + 1)`

D

`p n (p n + (1)/(2))`

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-SEQUENCE AND SERIES-Practice Exercise
  1. The sum of r terms of an A.P. is denoted by S(r ) and (S(m+1))/(S(n+1)...

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  2. The n^(th) term of an A.P is p and the sum of the first n terms is s. ...

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  3. If s(1), s(2), s(3)…..s(p) are the sums of n terms of 'p' A.P's whose ...

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  4. If a(1), a(2), a(3)…..a(n) are in A.P. with common difference d then s...

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  5. If S(1), S(2), S(3) be the sum of 10, 20, 30 terms respectively of an ...

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  6. The first, second and last terms of an A.P. are a, b, c respectively, ...

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  7. If the sum of the first ten terms of an A.P is four times the sum of i...

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  8. If a,b,c are in A.P then a((1)/(b) + (1)/(c )), b ((1)/(c ) + (1)/(a))...

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  9. If p, q, r are in A.P the p^(2) (q + r), q^(2) (r + p), r^(2) (p+q) ar...

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  10. If the A.M. between p^(th) and q^(th) terms of an A.P be equal to A.M ...

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  11. If n A.M's are inserted between two quantites a and b then their sum i...

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  12. If n A.M.'s are inserted between 4 and 96 then sum of n A.M.'s is

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  13. If n A.M.'s are inserted between 20 and 80 such that the ratio of firs...

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  14. Fifth term of G.P. is 2. The product of its first nine terms is

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  15. If (m+n)^(th) term and (m-n)^(th) terms of a G.P. are p and q respecti...

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  16. Let a(n) be the n^(th) term of G.P. If Sigma(n=1)^(100)a(2n)=alpha and...

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  17. If 4^(th), 7^(th), 10^(th) terms of a G.P. are p, q, r respectively th...

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  18. If l, m, n are the p^(th), q^(th), r^(th) terms of a G.P which are +ve...

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  19. If S=1 + a + a^(2) + ….+ oo (a lt 1) then the value of q=

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  20. If x= Sigma(n=0)^(oo) a^(n), y= Sigma(n=0)^(oo) b^(n), z= Sigma(n=0)^(...

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