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Find the sum of the first n terms of the series `1^3+3.2^2+3^3+3.4^2+5^2+3.6^2+....` when n is even

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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. Let a1,a2,a3,.......a11 be real number satisfying a1=15,27-2a2gt0 anda...

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  2. The interior angles of a polygon are in arithmetic progression. The sm...

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  3. Find the sum of the first n terms of the series 1^3+3.2^2+3^3+3.4^2+5^...

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  4. Find the sum of the first n terms of the series 1^3+3.2^2+3^3+3.4^2+5^...

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  5. Does there exist a GP containing 27,8 and 12 as three of its terms ? I...

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  6. The sum of the squares of three distinct real numbers, which are in GP...

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  7. Prove that the three successive terms of a GP will form the sides of ...

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  8. If (m+1)^th ,(n+1)^th and (r+1)^th terms in AP are in GP m,n,r are in ...

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  9. If p be the first of n arithmetic means between two numbers and q be t...

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  10. Show that 1^4/13+2^4/3.5+3^4/5.7+.....+n^4/((2n-1)(2n+1))=(n(4n^2+6n+5...

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  11. Solve the following equations for x and y log10xx+1/2log10xx+1/4log10x...

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  12. Find the sum of the series 1/1.3+2/(1.3.5)+3/(1.3.5.7)...upto infinit...

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  13. If sum(r=1)^nTr =n/8(n+1)(n+2)(n+3) then find sum(r=1)^n1/Tr

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  14. If 1,log9(3^(1-x)+2) and log3(4.3^x-1) are in AP , then x is equal to

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  15. If the sum of the first 2n terms of the AP 2,5,8.....is equal to the s...

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  16. If xin R , the number 5^(1+x)+5^(1-x),a/2,25^x+25^-xform an AP , then ...

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  17. If an AP a7=9 and a1a2a7 is least , then common difference is

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  18. Consider an infinite geometric series with first term a and common rat...

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  19. The value of a^(logb(x))=(where, a=0.2,b=sqrt5), x=(1/4+1/8+1/16+........

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  20. If a,b,c are in HP and agtcgt0, then 1/(b-c)-1/(a-b).

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