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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.`

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To find the sum of the first 24 terms of the arithmetic progression (A.P.) given that \( a_1 + a_5 + a_{10} + a_{15} + a_{20} + a_{24} = 225 \), we can follow these steps: ### Step 1: Express the terms in terms of \( a_1 \) and \( d \) The general term of an A.P. can be expressed as: \[ a_n = a_1 + (n-1)d \] Thus, we can express the required terms: ...
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Find the sum of first 24 terms of the A.P. a_1,a_2, a_3 ......., if it is inown that a_1+a_5+a_(10)+a_(15)+a_(20)+a_(24)=225.

Given that sequence of number a _(1), a _(2) , a_(3),……, a _(1005) which satisfy (a_(1))/( a _(1)+ 1) =(a_(2))/(a _(2) +3) = (a _(3))/(a _(3)+5) = …… = (a _(1005))/(a _(1005)+2009) a_1+a_2+a_3.......a_(1005)=2010 find the 21^(st) term of the sequence is equal to :

Knowledge Check

  • A sequence of number is represented as a_1, a_2, a_3,….a_n . Each number in the sequence (except the first and the last) is the mean of the first two adjacent numbers in the sequece. If a_(1) = 1 and a_5 = 3 , what is hte value of a_(3) ?

    A
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    B
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    C
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    D
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    Given that sequence of number a _(1), a _(2) , a_(3),……, a _(1005) which satisfy (a_(1))/( a _(1)+ 1) =(a_(2))/(a _(2) +3) = (a _(3))/(a _(3)+5) = …… = (a _(1005))/(a _(1005)+2009) a_1+a_2+a_3.......a_(1005)=2010

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