Question

         26,   22,   18,   14,   10,   6

Which algebraic expression represents the nth number in this sequence?

A.

−4n + 26

B.

4n + 22

C.

26n − 4

D.

−4n + 30

Answer 1

To find the algebraic expression that represents the nth number in the sequence \(26, 22, 18, 14, 10, 6\), we first observe the pattern in the sequence:

- The sequence starts at 26.
- Each subsequent term decreases by 4.

This indicates that the sequence is linear and can be expressed in the form of \(a_n = an + b\), where \(a\) is the common difference and \(b\) is the first term.

1. **Identify the common difference**: The difference between consecutive terms is \(22 - 26 = -4\), \(18 - 22 = -4\), etc. So, the common difference \(a = -4\).
2. **Initial term**: The first term of the sequence (\(n=1\)) is \(26\).

Thus, we can write the expression for the nth term like so:

\[
a_n = -4n + b
\]

To find \(b\), we set \(n=1\):
\[
a_1 = -4(1) + b = 26
\]
\[
-4 + b = 26 \implies b = 30
\]

So the algebraic expression for the nth term is:

\[
a_n = -4n + 30
\]

Now, we can match this expression to the options given:

A. \(-4n + 26\)

B. \(4n + 22\)

C. \(26n - 4\)

D. \(-4n + 30\)

The correct answer is:

**D. \(-4n + 30\)**.