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Let a(1), a(2),…. and b(1),b(2),…. be ar...

Let `a_(1), a_(2),….` and `b_(1),b_(2),….` be arithemetic progression such that `a_(1)=25`, `b_(1)=75` and `a_(100)+b_(100)=100`, then the sum of first hundred term of the progression`a_(1)+b_(1)`, `a_(2)+b_(2)`,…. is equal to

A

the difference between successive terms in progression 'a' is opposite of the difference in progression 'b'

B

`a_(n) + b_(n) = 100` for any n

C

`(a_(1) + b_(1)), (a_(2) + b_(2)), (a_(3) + b_(3)),`..... are in A.P.

D

`underset(r = 1)overset(100)sum (a_(r) + b_(r)) = 10000`

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ALLEN-SEQUENCE AND PROGRESSION-Exercise O-2
  1. If a, b, c are in AP, then (a - c)^(2) equals

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  2. If for an A.P. a1,a2,a3,........,an,........a1+a3+a5=-12 and a1a2a3=8,...

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  3. If the sum of the first 11 terms of an arithmetical progression equals...

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  4. Let s(1), s(2), s(3).... and t(1), t(2), t(3).... are two arithmetic s...

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  5. If x ∈ R and the numbers (5 ^ (1−x) +5^ (x+1) , a/2, (25^ x +25^ −x ...

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  6. Along a road lies an odd number of stones placed at intervals of 10 m....

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  7. In an A.P. with first term 'a' and the common difference d(a, d!= 0), ...

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  8. Let an, n in N is an A.P with common difference d and all whose terms ...

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  9. Let a(1), a(2),…. and b(1),b(2),…. be arithemetic progression such tha...

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  10. The arithmaeic mean of the nine numbers in the given set {9,99,999,….....

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  11. If (1 + 3 + 5 + .... " upto n terms ")/(4 + 7 + 10 + ... " upto n term...

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  12. If a != 1 and l n a^(2) + (l n a^(2))^(2) + (l n a^(2))^(3) + ... = 3 ...

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  13. The sum of the first three terms of an increasing G.P. is 21 and the s...

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  14. a, b, c are distinct positive real in HP, then the value of the expres...

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  15. An H.M. is inserted between the number 1/3 and an unknown number. If w...

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  16. If abcd = 1, where a,b,c and d are positive real numbers, then find th...

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  17. If 27 abc>= (a+b+c)^3 and 3a +4b +5c=12 then 1/a^2+1/b^3+1/c^5=10, w...

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  18. 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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