Answer :
To find the rule for the nth term of the sequence where the first term \( a_1 \) is 7 and the common difference \( d \) is -4 (since each term decreases by 4), we can use the formula for the nth term of an arithmetic sequence:
\[ a_n = a_1 + (n - 1) \cdot d \]
Substituting the given values \( a_1 = 7 \) and \( d = -4 \), we get:
\[ a_n = 7 + (n - 1) \cdot (-4) \]
Now, let's find \( a_8 \) when \( n = 8 \). Substitute \( n = 8 \) into the formula:
\[ a_8 = 7 + (8 - 1) \cdot (-4) \]
\[ a_8 = 7 + 7 \cdot (-4) \]
\[ a_8 = 7 - 28 \]
\[ a_8 = -21 \]
So, when \( n = 8 \), the 8th term (\( a_8 \)) of the sequence is -21.
