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The 1025th termm in the sequence are `1,22,4444,88888888,"…"`isA. `2^(9)`B. `2^(10)`C. `2^(11)`D. `2^(12) |
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Answer» The number of digits in each term of the sequence are `1,2,4,8,"…"` which are in GP. Let 1025th term is `2^(n)`. Then `1+2+4+8+"..."+2^(n-1)lt1025 le1+2+4+8+"..."+2^(n)` ` implies ((2-1)(1+2+2^(2)+2^(3)+"..."+2^(n-1)))/((2-1))lt1025` ` le ((2-1)(1+2+2^(2)+2^(3)+"..."+2^(n)))/((2-1))` ` implies 2^(n)-1lt1025 le2^(n+1)-1 implies 2^(n)lt1026 le 2^(n+1)"....(i)"` or `2^(n+1)ge 1026gt 1024` `implies 2^(n+1)gt2^(10) implies n+1gt10` ` therefore ngt9 therefore =10` [which is always satisfy Eq. (i)] Hence, (b) is the correct answer. |
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