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Statement 1 `4,8,16,` are in GP and 12,16,24 are in HP. Statement 2 If middle term is added in three consecutive terms of a GP, resultant will be in HP.A. Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1B. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1C. Statement 1 is true, Statement 2 is falseD. Statement 1 is false, Statement 2 is true |
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Answer» Correct Answer - A If a,b,c are in GP. Then, `b^(2)=ac` If middle term is added, then `a+b,2b " and " c+b` are in GP. `(I-II)/(II-III)=(a+b-2b)/(2b-(c+b)) " " [" here ",I=a+b,II=2b,III=c+b]` `=(a-b)/(b-c)=(ab-b^(2))/(b^(2)-bc)=(ab-ac)/(ac-bc)" " [:.b^(2)=ac]` `=(a(b-c)(a+b)(b+c))/(c(a-b)(a+b)(b+c))` `=(a(b^(2)-c^(2))(a+b))/(c(a^(2)-b^(2))(b+c))` `=(a(ac-c^(2))(a+b))/(c(a^(2)-ac)(b+c)),(a+b)/(b+c)=(I)/(II)` Hence, `a+b,2b,b+c` are in HP. Hence, both statements are true and Statement 2 is correct explanation for Statement 1. |
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