Answer:
The function that describes the arithmetic sequence is A(n) = 4n + 6
Step-by-step explanation:
The formula of the arithmetic sequence is a = a + (n - 1)d, where
- a is the first term of the sequence
- d is the common difference between each 2 consecutive terms
- n is the position of the number
∵ The terms of the sequence area 10, 14, 18, 22
∵ The first term is 10
∴ a = 10
∵ 14 - 10 = 4
∵ 18 - 14 = 4
∵ 22 - 18 = 4
∴ The common difference is 4
∴ d = 4
→ Substitute them in the formula above
∵ a = 10 + (n - 1)4
∴ a = 10 + n(4) - 1(4)
∴ a = 10 + 4n - 4
→ Add the like terms
∵ a = 4n + (10 - 4)
∴ a = 4n + 6
→ Write it in the form of the function A(n)
∴ A(n) = 4n + 6
∴ The function that describes the arithmetic sequence is A(n) = 4n + 6