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The sum of n ,2n ,3n terms of an A.P. ar...

The sum of `n ,2n ,3n` terms of an A.P. are `S_1S_2, S_3,` respectively. Prove that `S_3=3(S_2-S_1)dot`

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Let the sum of n, 2n, 3n terms of an A.P. be S_1, S_2 and S_3 , respectively, show that S_3 =3(S_2-S_1)

If the sums of n, 2n and 3n terms of an A.P. be S_(1), S_(2), S_(3) respectively, then show that, S_(3) = 3(S_(2) - S_(1)) .

If the first term, common ratio and the sum of first n terms of a G.P. be a, r and S_(n) respectively, find the value of S_(1) + S_(2) + S_(3) +….+S_(n) .

If S_1,S_2 and S_3 be respectively the sum of n, 2n and 3n terms of a G.P., prove that S_1(S_3-S_2)=((S_2)-(S_1))^2

The sum of n term of three A.P are S_1,S_2, and S_3 . The frist term of each is 1 and common diffrence are 1,2,3 repectively .Prove that S_1+S_3 =2 S_2.

If S_(1), S_(2), S_(3) be respectively the sums of n, 2n and 3n terms of a G.P., prove that, S_(1)(S_(3) - S_(2)) = (S_(2) - S_(1))^(2) .

If s_1 ,s_2 and s_3 are the sum of first n,2n,3n terms respectively of an arithmetic progression, then show that s_3=3(s_2-s_1) .

If S_1, S_2 and S_3 be respectively the sum of n, 2n and 3n terms of a G.P .Prove that S_1(S_3-S_2)=(S_2-S_1)^2 .

If s_1 be the sum of (2n+1) terms of an A.P and s_2 be the sum its odd terms, then prove that s_1:s_2=(2n+1):(n+1)

Let S_n denote the sum of first n terms of an A.P. If S_(2n)=3S_n , then find the ratio S_(3n)//S_ndot

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
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  3. The sum of n ,2n ,3n terms of an A.P. are S1S2, S3, respectively. Prov...

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  4. In a certain A.P., 5 times the 5th term is equal to 8 times the 8th ...

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  5. If x is a positive real number different from 1, then prove that the n...

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  6. Which term of the sequence 20 ,19 1/4, 18 1/2, 17 3/4,dot is the first...

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  7. If Sn=n P+(n(n-1))/2Q ,w h e r eSn denotes the sum of the first n term...

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  8. Find the sum sum(r=1)^n r(r+1)(r+2)(r+3)

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  10. Find the sum sum(r=1)^n r(r+1)(r+2)(r+3)

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  11. Find the sum 1+1/(1+2)+1/(1+2+3)+..........+1/(1+2+3+.........+n)dot

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  12. Find the sum to n terms of the series 1/(1 + 1^2 + 1^4) + 2/(1 + 2^2...

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  13. Find the sum to n terms of the series 3//(1^2xx2^2)+5//(2^2xx3^2)+7//(...

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  14. Find the sum sum(r=1)^n1/((a r+b)(a r+a+b))dot

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  15. If x=sum(n=0)^ooa^n , y=sum(n=0)^oob^n , z=sum(n=0)^ooc^n , w h e r e ...

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  16. If the sum of the series sum(n=0)^oor^n ,|r|<1 is s , then find the s...

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  17. Find the sum of the series sum(k=1)^(360)(1/(ksqrt(k+1)+(k+1)sqrt(k)))

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  19. Find the value of 11^2+12^2+13^2++20^2dot

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  20. Find the sum 2+5+10+17+26+. . . .

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