Permutations and Combinations

Permutations and Combinations

Question

The third term of a GP. is 4. Find the product of its first five terms.

Answer

Let a be the first  term and r be the common ratio
                straight t subscript 3 space equals space 4 space space space space space space space space rightwards double arrow space space space space space ar to the power of 3 minus 1 end exponent space equals space 4 space space rightwards double arrow space ar squared space equals space 4                 ...(i)
Product of first five terms = straight t subscript 1. space straight t subscript 2. space end subscript straight t subscript 3. space straight t subscript 4. space straight t subscript 5 space space equals space left parenthesis straight a right parenthesis space left parenthesis ar right parenthesis space left parenthesis ar squared right parenthesis space left parenthesis ar cubed right parenthesis space left parenthesis ar to the power of 4 right parenthesis
                                  = straight a to the power of 5 straight r to the power of 1 plus 2 plus 3 plus 4 end exponent equals space straight a to the power of 5 straight r to the power of 10 space equals space left parenthesis ar squared right parenthesis to the power of 5 space space equals space left parenthesis 4 right parenthesis to the power of 5 space equals space 1024   {By using (i)}

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