Question

Seventh term of an arithmetic sequence is 120 and its 8th term is 119. What is the 120th term of this sequence?

• A. 7
• B. 0
• C. 8
• D. 239

Answer 1

Answer:

A. 7

The 120th term of this arithmetic sequence is 7.

1. Identify the Common Difference ($d$)

The common difference is found by subtracting any term from the term that immediately follows it (the next term).

• 7th term ($x_7$) = $120$

• 8th term ($x_8$) = $119$

$d = x_8 - x_7 = 119 - 120 = \mathbf{-1}$

2. Use the Arithmetic Sequence Formula

The formula to find any specific term ($x_n$) from an already known term ($x_k$) is:
$x_n = x_k + (n - k)d$

We want to find the 120th term ($x_{120}$), and we can use the 8th term ($x_8 = 119$) as our reference:

• $n = 120$

• $k = 8$

• $x_8 = 119$

• $d = -1$

3. Calculate the Term

Substitute these values directly into the formula:
$x_{120} = 119 + (120 - 8) \times (-1)$

$x_{120} = 119 + (112) \times (-1)$

$x_{120} = 119 - 112$

$x_{120} = \mathbf{7}$