Given that the AP 10,6,2,-2 find the nth term

Answer 1

To find the \(n\)th term of the arithmetic progression (AP) given by the sequence \(10, 6, 2, -2\), we first need to identify the first term (\(a\)) and the common difference (\(d\)).

1. The first term \(a\) is \(10\).

2. The common difference \(d\) can be calculated by subtracting the first term from the second term:

   \[ d = 6 - 10 = -4 \]

The formula for the \(n\)th term of an arithmetic progression is given by:

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

Substituting the values of \(a\) and \(d\):

\[ a_n = 10 + (n - 1)(-4) \]

Now simplify the expression:

\[ a_n = 10 - 4(n - 1) \] \[ a_n = 10 - 4n + 4 \] \[ a_n = 14 - 4n \]

Therefore, the \(n\)th term of the arithmetic progression is:

\[ a_n = 14 - 4n \]