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If the sum of n terms of an A.P is cn (n...

If the sum of n terms of an A.P is cn (n-1)where `c ne 0` then the sum of the squares of these terms is

A

`a^(2)n^(2)(n-1)^(2)`

B

`(a^(2))/(6)n(n-1)(2n-1)`

C

`(2a^(2))/(3)n(n-1)(2n-1)`

D

`(2a^(2))/(3)n(n+1)(2n+1)`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Exercise
  1. If a , b, c, be in A.P. , b, c,d in G.P. and c.d.e.in H.P., then prov...

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  2. If (a+b)/(1-ab),b,(b+c)/(1-bc) are in AP, then a,(1)/(b),c are in

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  3. If the sum of n terms of an A.P is cn (n-1)where c ne 0 then the sum o...

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  4. Sum of the first p, q and r terms of an A.P are a, b and c, respectiv...

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  5. If Sn=1/1^3 +(1+2)/(1^3+2^3)+...+(1+2+3+...+n)/(1^3+2^3+3^3+...+n^3) T...

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  6. If a,b and c are in A.P. a,x,b are in G.P. whereas b, y and c are also...

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  7. If log(x+z)+log(x-2y+z)=2log(x-z)," then "x,y,z are in

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  8. If (1)/(a)+(1)/(c)+(1)/(a-b)+(1)/(c-b)=0, than prove that a,b,c are in...

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  9. If arithmetic mean of two positive numbers is A, their geometric mean ...

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  10. If (1-p)(1+3x+9x^2+27 x^3+81 x^4+243 x^5)=1-p^6,p!=1 , then the value ...

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  11. If a, b, c are in G.P, then loga x, logb x, logc x are in

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  12. If the sum of series 1+(3)/(x)+(9)/(x^(2))+(27)/(x^(3))+ . . .. " to "...

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  13. If H be the H.M. between a and b, then the value of (H)/(a)+(H)/(b) is

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  14. The sum of n terms of two arithmetic progressions are in the ratio 2n+...

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  15. If x = underset(n-0)overset(oo)sum a^(n), y= underset(n =0)overset(oo)...

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  16. Show that X^((1)/(2))*X^((1)/(4))*X^((1)/(8))... Upto oo = X

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  17. If a,b,c be in arithmetic progession, then the value of (a+2b-c) (2b+c...

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  18. If a, b, c are distinct positive real numbers in G.P and logca, logbc,...

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  19. If lta(n)gtandltb(n)gt be two sequences given by a(n)=(x)^((1)/(2^(n))...

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  20. The sum of the squares of three distinct real numbers which are in G...

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