Permutations and Combinations

Permutations and Combinations

Question

Find the indicated terms in the following sequence whose nth terms are :

space space straight a subscript straight n space equals space fraction numerator straight n left parenthesis straight n minus 2 right parenthesis over denominator straight n plus 3 end fraction

Answer

Here, straight a subscript straight n space equals space fraction numerator straight n left parenthesis straight n minus 2 right parenthesis over denominator straight n plus 3 end fraction semicolon space space straight a subscript 19
Putting n = 19, we get straight a subscript 19 space equals space fraction numerator 19 left parenthesis 9 minus 2 right parenthesis over denominator 19 plus 3 end fraction space equals space fraction numerator 19 cross times 17 over denominator 22 end fraction equals 323 over 22

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