Find the

14th term of a sequence where the first term is 3
and the common difference is -10

.

1 answer

To find the \( n \)-th term of an arithmetic sequence, you can use the formula:

\[ a_n = a_1 + (n - 1) \cdot d \]

where:

  • \( a_n \) is the \( n \)-th term,
  • \( a_1 \) is the first term,
  • \( d \) is the common difference,
  • \( n \) is the term number.

In this case:

  • \( a_1 = 3 \)
  • \( d = -10 \)
  • \( n = 14 \)

Now, plug these values into the formula:

\[ a_{14} = 3 + (14 - 1) \cdot (-10) \]

Calculating inside the parentheses:

\[ a_{14} = 3 + 13 \cdot (-10) \] \[ a_{14} = 3 - 130 \] \[ a_{14} = -127 \]

Therefore, the 14th term of the sequence is \(\boxed{-127}\).