Question

Find an explicit formula for the arithmetic sequence 10, -10, -30, -50, ...

a) aₙ = 10 - 20n
b) aₙ = 10 - 10n
c) aₙ = 10 - 30n
d) aₙ = 10 - 40n

Answer 1

To find the explicit formula for the arithmetic sequence 10, -10, -30, -50, ..., the first term (a1) is 10 and the common difference (d) is -20. The general formula is an = a1 + (n - 1)d, which simplifies to an = 10 - 20n. The correct answer is a) an = 10 - 20n.

Step-by-step explanation:

You're looking to find an explicit formula for the arithmetic sequence 10, -10, -30, -50, ... To find the formula, you need to identify the first term (a1) and the common difference (d) of the sequence.

The first term a1 is clearly 10, and the common difference d can be found by subtracting the first term from the second term: d = -10 - 10 = -20.

The general form for the explicit formula for an arithmetic sequence is an = a1 + (n - 1)d. Using a1 = 10 and d = -20, you get:

an = 10 + (n - 1)(-20)

You can further simplify this to:

an = 10 - 20n + 20

Combining like terms, the formula becomes:

an = 30 - 20n

So the correct answer is option a) an = 10 - 20n.