Question

A sequence has its first term equal to 4, and each term of the sequence is obtained by adding 2 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) = 2 and f(n) = f(n − 1) + 4; n > 1

f(1) = 4 and f(n) = f(n − 1) + 2n; n > 1

f(1) = 2 and f(n) = f(n − 1) + 4n; n > 1

f(1) = 4 and f(n) = f(n − 1) + 2; n > 1

Answer 1

The answer is the fourth option - f(1) = 4 and f(n) = f(n − 1) + 2; n > 1

The first term is 4, So, f(1) = 4
The difference between two consecutive integer = 2, so, n = (n-1) + 2
It would be Option D) f(1) = 4 and f(n) = f(n − 1) + 2; n > 1

Hope this helps!