Question

The fifth ninth and sixteenth terms of a linear sequence ( ap) are consecutive terms of an exponential sequence
1 find the common difference of the linear sequence in terms of the 1st term
2 show that the 21st 37th and 65th 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.

Answer 2

6:5

Answer 3

Ap a
Gp B
A +4d=b
A+8d=br
A+15d =br ^2
A=4/3d,b=49,r=7÷4
Picking value for d=3
A=3,b=12
Terms of g.p=12,21,147÷7

Answer 4

Ap a
Gp B
A +4d=b
A+8d=br
A+15d =br ^2
A=4/3d,b=49,r=7÷4
Picking value for d=3
A=3,b=12
Terms of g.p=12,21,147÷7