Permutations and Combinations

Permutations and Combinations

Question

The 5th, 8th and 11th terms of a GP. are p, q and s respectively. Show that q2 = ps.

Answer

Let a be the first term and r be the common ratio
                       straight t subscript 5 space equals space straight p space rightwards double arrow space ar to the power of 5 minus 1 end exponent space equals space straight p space rightwards double arrow space ar to the power of 4 space equals space straight p
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#6 {main}</pre>
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#6 {main}</pre>
Now,                  space space straight q squared space equals space left parenthesis ar to the power of 7 right parenthesis squared space equals space straight a squared straight r to the power of 14                              ...(i)
                         ps space equals space left parenthesis ar to the power of 4 right parenthesis space left parenthesis ar to the power of 10 right parenthesis space equals straight a squared straight r to the power of 14                         ...(ii)
From (i) and (ii), we have
                straight q squared space equals space ps
                  
                      

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