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? (1 point)

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

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? (1 point)
		
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

anonymous · Answer

this is an A.P
first term (a) = 4
common difference (d) = 2
Fn=a+(n-1)d
therefore,
Fn=4 + (n-1) 2
Fn = 4 +(2n-2)
F n = 4+2n-2= 2+2n
Fn= 2 (1+n)