Question

(b) The fifth, ninth and sixteenth terms of a linear sequence (a.p.) are consecutive terms of an exponential sequence (g.p.). (1) Find the common difference of the linear sequence in terms of the first term. () Show that the twenty-first, thirty-seventh and sixty-fifth terms of the linear sequence are consecutive terms of an exponential sequence whose common ratio is 7/4​

Answer 1

(a+8d)/(a+4d) = (a+15d)/(a+8d)
so, 3a=4d

1. a = 4/3 d

2. You can pick your values for a and d, say, a=4, d=3
So now form the desired terms, and show that they have a common ratio