Question

Given the recursive formula shown, what are the first 4 terms of the sequence?

f(1) = 6
f(n) = { f(n) = f(n-1) + 7 if n > 1
A) 6, 13, 20, 27
B) 6, 42, 294, 2,058
C) 6, -1, -8, -15
D) 7, 13, 19, 25

Answer 1

To find the first four terms of the sequence with the recursive formula f(1) = 6 and f(n) = f(n-1) + 7 if n > 1, we find that the sequence begins with 6, 13, 20, and 27.

Step-by-step explanation:

The question asks for the first four terms of a sequence defined by a recursive formula: f(1) = 6 and f(n) = f(n-1) + 7 for n > 1. To find the terms of the sequence, we start with the given first term and use the recursive formula to find subsequent terms.

• First term: f(1) = 6
• Second term: f(2) = f(1) + 7 = 6 + 7 = 13
• Third term: f(3) = f(2) + 7 = 13 + 7 = 20
• Fourth term: f(4) = f(3) + 7 = 20 + 7 = 27

So the first four terms of the sequence are 6, 13, 20, 27.