Write a rule for the nth term, where a1 is the first term and d = common difference. Then find an when n=8. Show you work. (7, 3, -1, -5....nth) a n ​ =a 1 ​ +(n−1)d a8 =



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.