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 \[-3\].You need to login to perform this action.
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