Question

The first and fifth terms of a sequence are given. Fill in the missing numbers if it is an arithmetic sequence. Then fill in the numbers if it is a geometric sequence. Write the explicit rule for each

function.
Arithmetic: f (n) = 4 + 80(n - 1)
Arithmetic
Geometric
+80 +80 +80 +80
84
164
244
4
12
36
108
×3
×3
×3
×3
324
324
Geometric: f(n) = 4(3)^-1

Answer 1

In summary, the arithmetic sequence is found by repeatedly adding 80 to each term, while the geometric sequence is found by repeatedly multiplying each term by 3. The explicit rules are f(n) = 4 + 80(n - 1) for the arithmetic sequence and f(n) = 4(3)^(n-1) for the geometric sequence.

Step-by-step explanation:

The arithmetic sequence is described by the explicit rule f(n) = 4 + 80(n - 1). To fill in the missing terms, we add 80 to each term starting from the first term (4):

• 4 (First term)
• 4 + 80 = 84 (Second term)
• 84 + 80 = 164 (Third term)
• 164 + 80 = 244 (Fourth term)
• 244 + 80 = 324 (Fifth term)

The geometric sequence given is f(n) = 4(3)^(n-1). To fill in the missing terms, we multiply each term by 3 starting from the first term (4):

• 4 (First term)
• 4 * 3 = 12 (Second term)
• 12 * 3 = 36 (Third term)
• 36 * 3 = 108 (Fourth term)
• 108 * 3 = 324 (Fifth term)

Therefore, the arithmetic sequence is 4, 84, 164, 244, 324, and the geometric sequence is 4, 12, 36, 108, 324.