Question

Write an explicit formula that represents the sequence defined by the following recursive formula

Answer 1

Answer:

The explicit formula is a$_{n}$ = 5 - 6n

Step-by-step explanation:

The explicit formula of the arithmetic sequence of the recursive formula

a$_{1}$ = first term; a$_{n}$ = a$_{n-1}$ + d is a$_{n}$ = a + (n - 1)d, where

• a is the first term

• d is the common difference between each two consecutive terms

• n is the position of the number

∵ The recursive formula is a$_{1}$ = -1 and a$_{n}$ = a$_{n-1}$ - 6

→ Compare it with the formula above

∴ a = -1 ⇒ 1st term

∴ d = -6 ⇒ common difference

→ Substitute them in the form of the explicit formula

∵ a$_{n}$  = -1 + (n - 1)(-6)

∴ a$_{n}$ = -1 + (-6)(n) - (-6)(1)

∴ a$_{n}$  = -1 + -6n - (-6)

∴ a$_{n}$ = -1 - 6n + 6

→ Add the like term

∴ a$_{n}$ = 5 - 6n

∴ The explicit formula is a$_{n}$ = 5 - 6n