Permutations and Combinations

Permutations and Combinations

Question

The seventh term of a GP. is 8 times the fourth term and 5th term is 48. Find the GP.

Answer

Let a be the first term and r be the common ratio.
According to the given condition,
                         space space space space straight t subscript 7 space equals space 8 straight t subscript 4 space space space rightwards double arrow space space ar to the power of 7 minus 1 end exponent space equals space 8 ar to the power of 4 minus 1 end exponent
rightwards double arrow                        ar to the power of 6 space equals space 8 ar cubed space space space space space space rightwards double arrow space space straight r cubed space equals space 8 space space space space space space space space space space space space space space space space rightwards double arrow space space space space space space space space space straight r space equals space 2
Also,                          straight t subscript 5 space equals space 48 space space space space space space space rightwards double arrow space space ar to the power of 5 minus 1 end exponent space equals space 48 rightwards double arrow space ar to the power of 4 space equals space 48 space rightwards double arrow space straight a left parenthesis 2 right parenthesis to the power of 4 space equals space 48 space rightwards double arrow space space straight a space equals space 48 over 16 space equals space 3

∴       G.P is 3, 3(2), 3(2)2,    ....... or        3, 6, 12,.......

More Chapters from Permutations and Combinations