Question

The formula for any arithmetic sequence is an = a1 + d(n - 1), where an represents the value of the nth term, a1 represents the value of the first term, d represents the common difference, and n represents the term number. What is the formula for the sequence 10, 8, 6, 4, ...?
an = 10 + 2( n - 1)
an = 2 + 10( n - 1)
an = -2 + 10( n - 1)
an = 10 + (-2)( n - 1)

Answer 1

Answer: an = 10 + (-2)( n - 1)

Step-by-step explanation:

In an arithmetic progression, the consecutive terms differ by a common difference. The formula for determining the nth term of an arithmetic sequence is expressed as

an = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

Looking at the given sequence,

a = 10

d = 8 - 10 = 6 - 8 = - 2

Therefore, the formula for the sequence is

an = 10 + (n - 1)- 2

an = 10 + (-2)( n - 1)

Answer 2

Answer:

an = 10 + (-2)(n-1)

Step-by-step explanation:

We are given from the sequence first term, a1 = 10

common difference, d = a2 - a1

Where; a2 = second term = 8

d = 8 - 10 = -2

From the formula, an = a1 + d(n - 1),

We substitute the value of a1 and d

therefore, an = 10 + (-2)(n - 1)