Arithmetic sequence problems
The 25th term of an arithmetic sequence where all terms are positive , is 100. If the sum of the first 49 terms of this sequence can be written in standard index form ( ), what is ab ?
The answer is 14.7.
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1 solution
Notice that any arithmetic sequence can be written in the form: ...( n +3 x ), ( n +2 x ), ( n + x ), ( n ), ( n - x ), ( n -2 x ), ( n -3 x )... , where all the x 's cancel down and where n is the middle term. We are asked to find the sum of all the terms between 1 and 49 inclusive; the median term can be found by 2 4 9 + 1 . This gives us 25; we are given that the 25th term is 100, and so can times 100 with the number of terms (49) to get the sum of this sequence. 49 and 100 multiply out to give 4900, which can be written as ( 4 . 9 × 1 0 3 ). 4.9= a and 3= b , hence ab =14.7