Question

Please write the equation of this sequence

Answer 1

Answer:
`a_(n) = (10)/(3) - (n)/(3)`

Explanation:

The sequence is decreasing by 1/3 each time. We can write the nth term of the sequence as:

aₙ = 3 - (n-1) × 1/3

Simplifying this expression, we get:

aₙ = 3 - (n/3 - 1/3)

aₙ = 3 - n/3 + 1/3

aₙ = 10/3 - n/3

To check this formula, let's substitute n = 1, 2, 3, and 4, and see if we get the correct terms:

a₁ = 10/3 - 1/3 = 3

a₂ = 10/3 - 2/3 = 8/3 =
`2(2)/(3)`

a₃ = 10/3 - 3/3 = 7/3 =
`2(1)/(3)`

a₄ = 10/3 - 4/3 = 2

a₅ = 10/3 - 5/3 = 5/3 =
`1(2)/(3)`

Therefore, the equation of the sequence is
`a_(n) = (10)/(3) - (n)/(3)`