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Find the two-hundredth term a(200) of th...

Find the two-hundredth term `a_(200)` of the sequence: `2;5;8;11.......`

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The correct Answer is:
C
`:. S_(n)=1+22+333+"..."+ubrace(" nnn""...."n)_(" n terms ")`
`:. S_(n)-S_(n-1)=ubrace(" nnn""...."n)_(" n times ")=ubrace(111"...."1)_(" n times ")`
`=n(10^(n-1)+10^(n-2)+"….."+10+1)=(n(10^(n)-1))/(10-1)`
`:. 9(S_(n)-S_(n-1))=n(10^(n)-1)`
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ARIHANT MATHS-SEQUENCES AND SERIES-Exercise (Single Option Correct Type Questions)
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  2. ABC is a right-angled triangle in which angleB=90^(@) and BC=a. If n p...

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  3. Find the two-hundredth term a(200) of the sequence: 2;5;8;11.......

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  4. If a,b,c are in GP, show that the equations ax^(2)+2bx+c=0 and dx^(2)+...

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  5. Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+............

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  6. If in a triangle PQR; sin P, sin Q, sin R are in A.P; then (A)the alt...

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  7. Let a1, a2, ,a(10) be in A.P. and h1, h2, h(10) be in H.P. If a1=h1=2...

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  8. If I(n)=int(0)^(pi)(1-sin2nx)/(1-cos2x)dx then I(1),I(2),I(3),"….." ar...

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  9. Find the value of lambda the equation is 5x+y+lambda=0 where x=1 and y...

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  10. The sum to infinity of the series 1+2(1-(1)/(n))+3(1-(1)/(n))^(2)+ ....

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  11. If log(3)2,log(3)(2^(x)-5) and log(3)(2^(x)-7/2) are in A.P., then x i...

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  12. If x,y,z be three positive prime numbers. The progression in which sqr...

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  13. If n is an odd integer greater than or equal to 1, then the value of n...

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  14. If the sides of a right angled triangle are in A.P then the sines of t...

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  15. The 6th term of an AP is equal to 2. The value of the common differenc...

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  16. If the arithmetic progression whose common difference is nonzero the ...

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  17. The coefficient of x^(n) in the expansion of (1+x)(1-x)^(n) is

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  18. Consider the pattern shown below: {:(" Row ",1,1,,,),(" Row ",2,3,5,...

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  19. Let a(n) be the nth term of an AP, if sum(r=1)^(100)a(2r)= alpha " and...

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  20. If a(1),a(2),a(3),a(4),a(5) are in HP, then a(1)a(2)+a(2)a(3)+a(3)a(4)...

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