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Consider the sequence S=7+13+21+31+".......

Consider the sequence `S=7+13+21+31+".....+"T_(n)` , find the value of `T_(70)`.

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`S=7+13+21+31+".....+"T_(n)`
`(S=ul " " ul7+ul13+ul21ul+".....+"ulT_(n-1)+ulT_(n))/(0=7+6+8+10+".....+" " n terms "-T_(n))`
`T_(n)=7+6+8+10+".....+"" n terms "`
`T_(n)=7+{6+8+10+".....+"" (n-1) terms "}`
`T_(n)=7+((n-1))/(2) (12+(n-2)2)`
`T_(n)=7+((n-1))/(2)(8+2n)`
`T_(n)=7+(n-1)(4+n)`
`T_(70)=7+69xx74=7+5106=5113`.
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ARIHANT MATHS-SEQUENCES AND SERIES-Exercise (Subjective Type Questions)
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  2. If 1/1^2+1/2^2+1/3^2+...oo=pi^2/6 then value of 1-1/2^2+1/3^2-1/4^2+.....

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  3. If the arithmetic mean of a(1),a(2),a(3),"........"a(n) is a and b(1),...

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  4. If a(1),a(2),a(3),"........" is an arithmetic progression with common ...

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  5. If t(1)=1,t(r )-t( r-1)=2^(r-1),r ge 2, find sum(r=1)^(n)t(r ).

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  6. Prove that I(1),I(2),I(3)"..." form an AP, if (i) I(n)=int(0)^(pi)(...

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  7. Consider the sequence S=7+13+21+31+".....+"T(n) , find the value of T(...

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  8. Find value of (x+(1)/(x))^(3)+(x^(2)+(1)/(x^(2)))^(3)+"........"+(x^(n...

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  9. If a(m) be the mth term of an AP, show that a(1)^(2)-a(2)^(2)+a(3)^(2)...

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  10. If three unequel numbers are in HP and their squares are in AP, show ...

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  11. Ifa(1),a(2),a(3),"........",a(n) are in AP with a(1)=0, prove that (a(...

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  12. Balls are arranged in rows to form an equilateral triangle. The first ...

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  13. If theta(1),theta(2),theta(3),".......",theta(n) are in AP whose commo...

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  14. Show that,(1+5^(-1))(1+5^(-2))(1+5^(-4))(1+5^(-8))"....."(1+5^(-2n))=(...

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  15. Evaluate S=sum(n=0)^n(2^n)/((a^(2^n)+1) (where a>1).

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  16. Find the sum to infinite terms of the series tan^(-1)((1)/(3))+tan^(-1...

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  17. Find the sum to n terms, whose nth term is tan[alpha+(n-1)beta]tan (al...

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  18. If sum(r=1)^(n)T(r)=(n)/(8)(n+1)(n+2)(n+3)," find "sum(r=1)^(n)(1)/(T(...

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  19. If s1,s2,s3 denote the sum of n terms of 3 arithmetic series whose fir...

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  20. The friends whose ages from a G.P. divide a certain sum of money in pr...

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