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Given a geometric sequence with second term 12 and ninth term 64. Determine the value of r. Find the value of a. Determine the general formula of the sequence.
in Mathematics by Diamond (62,244 points) | 73 views

1 Answer

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ar^n-1 for any term

Therefore 2nd term, ar^2-1 = ar

                                                ar = 12..........(1)

                  9nth term, ar^9-1 = ar^8

                                                  ar^8 = 64........(2)

Solving simultaneously,

                             

                                          ar = 12..........(1), a = 12/r

                                      subst into 2,     12/r x r^8 = 64

                                                                 12 x r^-1 x r^8 = 64

                                                                       12 x r^7  = 64

                                                                                 r^7 = 64/12 = 16/3

                                                                                          r = (16/3)^(1/7) = 1.27

                                                                    a = 12/r

                                                                     a = 12/1.27 = 9.45

                                                                                 Tn = 9.45(16/3)^(n-1)
by Diamond (42,470 points)

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