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11th Class Mathematics Sequence and Series Question Bank Sequence and Series (A.P., G.P. and H.P.)

  • question_answer
    The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.

    A)  - 13, - 8, - 3               

    B)  - 24, - 18, -12

    C)  6, 12, 18                     

    D)  0, 2, 4

    Correct Answer: A

    Solution :

    (a): Let a be the first term and. d the common difference of an AP, Given, \[{{a}_{4}}+{{a}_{8}}=24\]     (By given condition) \[\Rightarrow (a+3d)+(a+7d)=24\]                      \[[\because {{a}_{n}}=a+(n-1)d]\] \[2a+10d=24\]  \[\Rightarrow a+5d=12\]???..(i) Also, \[{{a}_{6}}+{{a}_{10}}=44\]      (By given condition) \[\Rightarrow (a+5d)+(a+9d)=44\]     \[\Rightarrow 2a+14d=44\] \[\Rightarrow a+7d=22\]             ???????.(ii) On subtracting Eq. (i) from Eq. (ii), we get \[2d=10\Rightarrow d=5\Rightarrow a=12-25=-13\] Hence, the first three terms are \[a,(a+d),(a+2d)\] i.e., \[-13,(-13+5)\] and \[(-13+2\times 5)\] i.e., \[-13,-8\]and \[-3\].


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