The 5th,9th and 16th terms of a linear sequence are consecutive terms of an exponential sequence G.P. find the common difference in terms of The first term
since AP has a constant difference, and GP has a constant ratio,
A9/a5 = a16/a9
(a+8d)^2 = (a+4d)(a+15d)
d = 3/4 a
so, for example, if a = 4, then d = 3 and we have
AP: 4,7,10,13,16,19,22,25,28,31,34,37,40,43,46,49
GP: 16,28,49 (r = 7/4)