Question

Find the 10th term of the sequence defined by the given rule. Assume that the domain of each function is the set of whole numbers greater than 0.

f(1) = 4, f(n)=f(n-1) + 13. What is the tenth term?
a) 114
b) 117
c) 130
d) 127

Answer 1

d) 127. The 10th term of the sequence is 127.

Step-by-step explanation:

To find the 10th term of a sequence defined by the rule f(1) = 4 and f(n) = f(n-1) + 13, we can use the recursive formula.

The first term is given as 4. To find the 10th term, we start with the first term and add 13 repeatedly 9 more times:

f(2) = f(1) + 13 = 4 + 13 = 17,

f(3) = f(2) + 13 = 17 + 13 = 30,

f(4) = f(3) + 13 = 30 + 13 = 43,

and so on.

Continuing this pattern, we find that the 10th term is 127 (d).