Find the nth term of the following

-7,-2,3,8

1 answer

To find the nth term of the sequence \(-7, -2, 3, 8\), let's first analyze the pattern.

  1. Identify the differences between consecutive terms:
    • From \(-7\) to \(-2\): difference = \( -2 - (-7) = 5\)
    • From \(-2\) to \(3\): difference = \(3 - (-2) = 5\)
    • From \(3\) to \(8\): difference = \(8 - 3 = 5\)

All the differences are constant and equal to \(5\), which indicates that this sequence is an arithmetic sequence with a common difference of \(5\).

  1. The formula for the nth term of an arithmetic sequence is:

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

Where:

  • \(a_1\) is the first term of the sequence.
  • \(d\) is the common difference.
  • \(n\) is the term number.
  1. For this sequence:
  • \(a_1 = -7\)
  • \(d = 5\)

Plugging in these values:

\[ a_n = -7 + (n - 1) \cdot 5 \]

  1. Simplifying this expression:

\[ a_n = -7 + 5n - 5 \] \[ a_n = 5n - 12 \]

So the nth term of the sequence is:

\[ \boxed{5n - 12} \]