InterviewSolution
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InterviewSolution
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Which of the following form of an AP ? Justify Your answer. (i) `-1,-1,-1,-1, …` (ii) `0, 2, 0, 2, …` (iii) `1, 1, 2, 2, 3, 3, … ` (iv) `11, 22, 33, … ` (v) `(1)/(2),(1)/(3),(1)/(4), … ` (vi) `2, 2^(2), 2^(3), 2^(4)` (vii) `sqrt(3),sqrt(12),sqrt(27),sqrt(48), ...` |
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Answer» (i) Here, `t_(1)=1, t_(2)= -1, t_(3)= -1` and `t_(4)= -1` `t_(2)-t_(1)= -1+1=0` `t_(3)-t_(2)= -1+1=0` `t_(4)-t_(3)= -1+1=0` Clearly, the difference of successive terms is same, therefore given list of numbers form an AP. (ii) Here, `t_(1)=0, t_(2)= 2, t_(3)= 0` and `t_(4)= 2` `t_(2)-t_(1)= 2-0=2` `t_(3)-t_(2)= 0-2= -2` `t_(4)-t_(3)= 2-0=2` Clearly, the difference of successive terms is not same, therefore given list of numbers does not form an AP. (iii) Here, `t_(1)=1, t_(2)= 1, t_(3)= 2` and `t_(4)= 2` `t_(2)-t_(1)= 1-1=0` `t_(3)-t_(2)= 2-1=1` `t_(4)-t_(3)= 2-2=0` Clearly, the difference of successive terms is not same, therefore given list of numbers does not form an AP. (iv) Here, `t_(1)=11, t_(2)= 22` and `t_(3)= 33` `t_(2)-t_(1)= 22-11=11` `t_(3)-t_(2)= 33-22=11` `t_(4)-t_(3)= 33-22=11` Clearly, the difference of successive terms is same, therefore given list of numbers form an AP. (v) Here, `t_(1)=(1)/(2), t_(2)= (1)/(3)` and `t_(3)= (1)/(4)` `t_(2)-t_(1)= (1)/(3)-(1)/(2)=(2-3)/(6)=(1)/(6)` `t_(3)-t_(2)=(1)/(4)-(1)/(3)=(3-4)/(12)=(1)/(12)` Clearly, the difference of successive terms is not same, therefore given list of numbers does not form an AP. (vi) `2, 2^(2), 2^(3), 2^(4), ...` i.e.,`2, 4, 8, 16, ...` Here, `t_(1)=2, t_(2)= 4, t_(3)= 8` and `t_(4)= 16` `t_(2)-t_(1)= 4-2=2` `t_(3)-t_(2)= 8-4= 4` `t_(4)-t_(3)= 16-8=8` Clearly, the difference of successive terms is not same, therefore given list of numbers does not form an AP. (vii) `sqrt(3),sqrt(12),sqrt(27),sqrt(48), ...` i.e., `sqrt(3),2sqrt(3),3sqrt(3),4sqrt(3), ...` Here, `t_(1)=sqrt(3), t_(2)= 2sqrt(3), t_(3)= 3sqrt(3)` and `t_(4)= 4sqrt(3)` `t_(2)-t_(1)= 2sqrt(3)-sqrt(3)=sqrt(3)` `t_(3)-t_(2)= 3sqrt(3)-2sqrt(3)=sqrt(3)` `t_(4)-t_(3)= 4sqrt(3)-3sqrt(3)=sqrt(3)` Clearly, the difference of successive terms is same, therefore given list of numbers form an AP. |
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