The first five terms of the given arithmetic sequence are:
54, 45, 36, 27, 18 (First option)
The arithmetic sequence is given as follows,
f(n) = f(n-1) - 9 ............ (1)
Also, f(1) = 54 .............. (2)
Now, for finding the first five term of this arithmetic sequence, we will substitute n as 1, 2, 3, 4, and 5 one by one. Using the above formula for the arithmetic sequence, we can deduce the first five terms.
f(1) is the first term of the sequence which is already provided as 54.
Now, putting n=2 in equation (1), we get,
f(2) = f(2-1) - 9
f(2) = f(1) - 9
Substitute f(1) = 54 from equation (2)
⇒ f(2) = 54 - 9
f(2) = 45
To find the third term of the arithmetic sequence, put n = 3 in equation (1)
f(3) = f(3-1) - 9
f(3) = f(2) - 9
⇒ f(3) = 45 - 9
f(3) = 36
Similarly, we can find the fourth and fifth terms of the arithmetic sequence by substituting n = 4 and n = 5 respectively.
∴ f(4) = f(3) - 9
⇒ f(4) = 36 - 9
f(4) = 27
Likewise, f(5) = f(4) - 9
⇒f(5) = 27 - 9
f(5) = 18
Thus, using the recursive formula, the first five terms of the arithmetic sequence are deduced to be:
54, 45, 36, 27, 18
Learn more about arithmetic sequence here:
brainly.com/question/15412619
#SPJ1
