Permutations and Combinations

Question

Find the sum of the indicated terms of each of the following CP’s:

3, 6, 12, ........; 7 terms

Answer

The given sequence is: 3, 6, 12,........
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$straight S subscript 7 space equals space fraction numerator straight a left parenthesis straight r to the power of 7 minus 1 right parenthesis over denominator straight r minus 1 end fraction space equals space fraction numerator 3 left parenthesis 2 to the power of 7 minus 1 right parenthesis over denominator 2 minus 1 end fraction space equals space 3 left parenthesis 128 minus 1 right parenthesis space equals space 3 left parenthesis 127 right parenthesis space equals space 381$