The fifth,ninth and sixteenth terms of a linear sequence and

The fifth,ninth and sixteenth terms of a linear sequence and consecutive terms of an exponential sequence,find the common difference of the linear sequence in terms of the first term, show that the twenty one, thirty seventh and sixty fifth term of the linear sequence are consecutive terms of an exponential sequence whose common ratio is 7 over 4

5 answers

I assume you meant that the 3 terms of the AP and the three terms of the GP are equal. So, if the AP starts with a, and the GP terms start with b, then
a+4d = b
a+8d = br
a+15d = br^2
a = 4/3 d, b = 4a, r = 7/4
So, pick a convenient value for d, such as 3. Then
a=3, b=12
the three terms of the GP are 12, 21, 147/4
You can figure out the other answers, since you know the sequences.

What is the 5th term of the linear sequence

I agreed to your solving

Thanks

Thanks for solving