Question

Write down in terms of n an expression for the nth term of the sequence -7 -12 -17 -22 -27

Answer 1

In this sequence, each term is obtained by subtracting 5 from the previous term. So, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n-1)d

where a1 is the first term, d is the common difference, and n is the term number we want to find.

In this case, a1 = -7, d = -5 (since we're subtracting 5 from each term to get the next one), and we want to find the nth term. So, plugging in these values, we get:

an = -7 + (n-1)(-5)

Simplifying, we get:

an = -7 - 5n + 5

an = -2 - 5n

Therefore, the expression for the nth term of the sequence is -2 - 5n.

Answer 2

`a_(n)` = - 5n - 2

Explanation:

there is a common difference between consecutive terms , that is

a₂ - a₁ = - 12 - (- 7) = - 12 + 7 = - 5

a₃ - a₂ = - 17 - (- 12) = - 17 + 12 = - 5

a₄ - a₃ = - 22 - (- 17) = - 22 + 17 = - 5

a₅ - a₄ = - 27 - (- 22) = - 27 + 22 = - 5

this indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + d(n - 1)

a₁ is the first term and d the common difference

here a₁ = - 7 and d = - 5 , then

`a_(n)` = - 7 - 5(n - 1) = - 7 - 5n + 5 = - 5n - 2