Question

Write a function to describe each arithmetic sequence
10, 14, 18, 22

Answer 1

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$_{n}$ = 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$_{n}$ = 10 + (n - 1)4

∴ a$_{n}$ = 10 + n(4) - 1(4)

∴ a$_{n}$ = 10 + 4n - 4

→ Add the like terms

∵ a$_{n}$ = 4n + (10 - 4)

∴ a$_{n}$ = 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