The first five terms of the given arithmetic sequence are:
1/5, 2/5, 3/5, 4/5, 1 (Fourth option)
The arithmetic sequence is given as follows,
f(n) = f(n-1) + 1/5 ............ (1)
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.
It is already given that f(1) = 1/5 ......... (2)
f(1) is the first term of the sequence.
Now, putting n=2 in equation (1), we get,
f(2) = f(2-1) + 1/5
f(2) = f(1) + 1/5
Substitute f(1) = 1/5 from equation (2)
⇒ f(2) = 1/5 + 1/5
f(2) = 2/5
To find the third term of the arithmetic sequence, put n = 3 in equation (1)
f(3) = f(3-1) + 1/5
f(3) = f(2) + 1/5
⇒ f(3) = 2/5 + 1/5
f(3) = 3/5
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) + 1/5
⇒ f(4) = 3/5 + 1/5
f(4) = 4/5
Likewise, f(5) = f(4) + 1/5
⇒f(5) = 4/5 + 1/5
f(5) = 1
Thus, using the recursive formula, the first five terms of the arithmetic sequence come out to be:
1/5, 2/5, 3/5, 4/5, 1
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