The fifth, ninth and sixteenth term of a Linear sequence are the consecutive term of an exponential sequence. Find the common difference of the linear sequence. Also show that the 21st, 37th and 65th terms of the sequence are consecutive terms of the exponential sequence whose common ratio is =7/4

= 4n + 2

Step-by-step explanation:

There is a common difference d between consecutive terms in the sequence, that is

d = 10 - 6 = 14 - 10 = 18 - 14 = 22 - 18 = 4

This indicates the sequence is arithmetic with n th term

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 6 and d = 4, thus

= 6 + 4(n - 1) = 6 + 4n - 4 = 4n + 2