Question

Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.

-6, -5, -4, -3, ...

Answer 1

The given sequence is an arithmetic sequence with a common difference of 1. The expression for the nth term is an = n - 7.

Step-by-step explanation:

The sequence given is an arithmetic sequence where each term increases by 1. To find an expression for the nth term of this sequence, you use the general form for an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference between the terms. For the sequence -6, -5, -4, -3, ... the first term, a1, is -6 and the common difference, d, is 1. The expression for this sequence is then an = -6 + (n - 1)(1), which simplifies to an = -6 + n - 1, and then to an = n - 7.

Answer 2

The expression to describe this sequence is Aₙ = (n - 1) * 1 - 6

Step-by-step explanation:

1. Let's write an expression to describe the sequence which first four terms are as follows:

- 6, -5, -4, - 3.....

Aₙ = (n - 1) * 1 - 6; A₁ = - 6

A₁ = (n - 1) * 1 - 6 = (1 - 1) * 1 - 6 = 0 * 1 - 6 ⇒A₁ = - 6

A₂ = (n - 1) * 1 - 6 = (2 - 1) * 1 - 6 = 1 * 1 - 6⇒ A₁ = - 5

A₃ = (n - 1) * 1 - 6 = (3 - 1) * 1 - 6 = 2 * 1 - 6⇒ A₁ = - 4

A₄ = (n - 1) * 1 - 6 = (4 - 1) * 1 - 6 = 3 * 1 - 6⇒ A₁ = - 3

A₅ = (n - 1) * 1 - 6 = (5 - 1) * 1 - 6 = 4 * 1 - 6⇒ A₁ = - 2

A₆ = (n - 1) * 1 - 6 = (6 - 1) * 1 - 6 = 5 * 1 - 6⇒ A₁ = - 1

A₇ = (n - 1) * 1 - 6 = (7 - 1) * 1 - 6 = 6 * 1 - 6⇒ A₁ = 0