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For arithmetic sequence a(1),a(2),a3 ......

For arithmetic sequence `a_(1),a_(2),a_3` ........ If `a_(1)+a_(5)+a_(10)+a_(15)+a_(20)+a_(24)= 225` then `s_(24) = ............ `

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Find the sum of first 24 terms of the A.P. a_(1) , a_(2), a_(3) ...., if it is know that a_(1) + a_(5) + a_(10) + a_(15) + a_(20) + a_(24) = 225

If the arithmetic mean of a_(1),a_(2),a_(3),"........"a_(n) is a and b_(1),b_(2),b_(3),"........"b_(n) have the arithmetic mean b and a_(i)+b_(i)=1 for i=1,2,3,"……."n, prove that sum_(i=1)^(n)(a_(i)-a)^(2)+sum_(i=1)^(n)a_(i)b_(i)=nab .

Let b_(i)gt1" for "i=1,2,"......",101 . Suppose log_(e)b_(1),log_(e)b_(2),log_(e)b_(3),"........"log_(e)b_(101) are in Arithmetic Progression (AP) with the common difference log_(e)2 . Suppose a_(1),a_(2),a_(3),"........"a_(101) are in AP. Such that, a_(1)=b_(1) and a_(51)=b_(51) . If t=b_(1)+b_(2)+"........."+b_(51)" and " s=a_(1)+a_(2)+"........."+a_(51) , then

Let a_(1),a_(2),"...." be in AP and q_(1),q_(2),"...." be in GP. If a_(1)=q_(1)=2 " and "a_(10)=q_(10)=3 , then

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Find the respective terms for the following Aps: (i) a_(1) =2, a_(3) = 26 find a_(2) (ii) a_(2) =13, a_(4) = 3 find a_(1), a_(3) (iii) a_(1) =5, a_(4) = -22 find a_(1),a_(3),a_(4),a_(5)

Suppose four distinct positive numbers a_(1),a_(2),a_(3),a_(4) are in G.P. Let b_(1)=a_(1),b_(2)=b_(1)+a_(2),b_(3)=b_(2)+a_(3)andb_(4)=b_(3)+a_(4) . Statement -1 : The numbers b_(1),b_(2),b_(3),b_(4) are neither in A.P. nor in G.P. Statement -2: The numbers b_(1),b_(2),b_(3),b_(4) are in H.P.

For arithmetic sequence a_(8) =23 common difference d = 5 then a = ...............

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KUMAR PRAKASHAN-OBJECTIVE SECTION AS PER NEW PAPER SCHEME -Sequence and Series (Fill in the blanks )
  1. For arithmetic sequence a = 2 and a5 = 14 then d = ........

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  2. For arithmetic sequence a(8) =23 common difference d = 5 then a = .......

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  3. For arithmetic sequence

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  4. For an A.P a = 20 and l = 97 then S(20)= ..........

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  5. If a, b, and c are in A.P then (a + 2b -c) . ( 2b +c-a) . (c+a-b) = .....

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  6. For arithmetic sequence a(1),a(2),a3 ........ If a(1)+a(5)+a(10)+a(15)...

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  7. If 25, x - 6 and x - 12 are in G.P then x = .......... or ......... .

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  8. Third term of G.P. is 3 then product of its first 5 terms is ............

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  9. Eighth term of G.P is 128 and common ratio is r = 2 then product of fi...

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  10. For an G.P. a = 16 and fifth term is 81 then common ratio ........

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  11. How many terms of G.P. 3, 3^2, 3^3, … are needed to give the sum 120?

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  12. For an geometric seq. (5)/2,(5)/(4),(5)/8.......a(n) = ............. .

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  13. A1 and A2 are arithmetic mean between a and b also G1 and G2 are geome...

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  14. For numbers 6 and 24, A - G = ...... .

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  15. 10 is Geometric mean between 5 and x then x = ......... Where x in R^(...

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  16. 12 is arithmetic mean between x and 22 then x = ............

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  17. 10 arithmetic mean between a and b are A(1),A(2),A(3).........A(10) th...

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  18. If sumn = 55 then sumn^2 . = ...............

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  19. sum(r=1)^n(2r+1)=...... .

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  20. Sum of the series 1-(1)/(2)+1/(2^2)-1/(2^3)+............oo=.........

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