Question

A sequence has its first term equal to 3, and each term of the sequence is obtained by adding 5 to the previous term. If f(n) represents the nth term of the sequence, which of the following recursive functions best defines this sequence?

f(1) = 3 and f(n) = f(n − 1) + 5; n > 1
f(1) = 5 and f(n) = f(n − 1) + 3; n > 1
f(1) = 3 and f(n) = f(n − 1) + 5n; n > 1
f(1) = 5 and f(n) = f(n − 1) + 3n; n > 1

Answer 1

f(1) = first term = 3 so its either a or c
when N > 1 ( that is from second term on) you add 5
So the answer is a

Answer 2

Here, first term is 3, So, f(1) = 3

Now, difference between two consecutive integer = 5,
So, n = (n-1) + 5

In short, Your Answer would be Option A) f(1) = 3 and f(n) = f(n − 1) + 5; n > 1

Hope this helps!