InterviewSolution
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InterviewSolution
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If first and `(2n-1)^th` terms of an AP, GP. and HP. are equal and their nth terms are a, b, c respectively, then(a) a=b=c (b)a+c=b (c) a>b>c and `ac-b^2=0` (d) none of theseA. `a = b = c`B. `a ge b ge c`C. `a + c = b`D. `ac - b^(2) = 0` |
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Answer» Correct Answer - A::B::D Since, first and `(2n -1)th` terms are equal. Let first term be x and `(2n -1)`th term be y shoe middle term is `l_(n)`. Thus, in arithmetic progression, `t_(n) = (x + y)/(2) = a` In geometric progression, `t_(n) = sqrt(xy) = b` In harmonic progression, `t_(n) = (2xy)/(x + y) = c` `rArr b^(2) = ac and a gt b gt c` [using `AM gt GM gt HM`] Here, equality holds (i.e., `a = b =c`) only if all terms are same. Hence, options (a), (b) and (d) are correct |
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