Question

Determine the expanded and simplified general term for the arithmetic sequence whose 5th term is 10, and consecutive terms decrease by 4.

a) ( aₙ = 14 - 4n )
b) ( aₙ = 14 + 4n )
c) ( aₙ = 10 - 4n )
d) ( aₙ = 10 + 4n )

Answer 1

The general term for this arithmetic sequence is aₙ = 14 - 4n.

Step-by-step explanation:

The general term for an arithmetic sequence is given by the formula:

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 consecutive terms.

In this case, we are given that the 5th term is 10, and consecutive terms decrease by 4. So we have:

aₙ = a₁ + (5-1)(-4)

aₙ = a₁ - 4(4)

aₙ = a₁ - 16

We can simplify this to:

aₙ = 14 - 4n

Therefore, the correct answer is (a) (aₙ = 14 - 4n).