Question

examine the sequence of numbers below.
-7, -16, -25, -34, -43
which algebraic expression represents the nth number in this sequence?
drag these tiles and drop them in the correct blank above
= 16n + 9
= -9n + 2
= 8n + 14
= -7n + 9

Explanation:

Step1: Find the common difference

The sequence is \(-7, -16, -25, -34, -43\). Let's find the difference between consecutive terms.
\(-16 - (-7) = -16 + 7 = -9\)
\(-25 - (-16) = -25 + 16 = -9\)
\(-34 - (-25) = -34 + 25 = -9\)
\(-43 - (-34) = -43 + 34 = -9\)
So the common difference \(d = -9\).

Step2: Identify the first term

The first term \(a_1 = -7\).

Step3: Use the arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n = a_1 + (n - 1)d\).
Substitute \(a_1 = -7\) and \(d = -9\) into the formula:
\(a_n = -7 + (n - 1)(-9)\)
Expand the expression:
\(a_n = -7 - 9n + 9\)
Simplify:
\(a_n = -9n + 2\)

Answer:

\(-9n + 2\)