39) Write an explicit formula for the recursive formula, $$ a_{1}=-2, a_{n}=a_{n-1}-12, n \geq 2 $$ $$ a_{n}= $$

Question

UpStudy AI · Accepted Answer

To solve the recurrence relation
$$
a_{1} = -2, \quad a_{n} = a_{n-1} - 12,\quad n \geq 2,
$$
follow these steps:

1. Recognize that the sequence is arithmetic with a common difference $$ d = -12 $$.

2. The formula for the $$ n $$-th term of an arithmetic sequence is
$$
a_{n} = a_{1} + (n-1)d.
$$

3. Substitute $$ a_{1} = -2 $$ and $$ d = -12 $$ into the formula:
$$
a_{n} = -2 + (n-1)(-12).
$$

4. Simplify the expression:
$$
a_{n} = -2 - 12(n-1) = -2 - 12n + 12 = 10 - 12n.
$$

Thus, the explicit formula for the sequence is
$$
a_{n} = 10 - 12n.
$$
The explicit formula for the sequence is $$ a_{n} = 10 - 12n $$.

39) Write an explicit formula for the recursive formula, \( a_{1}=-2, a_{n}=a_{n-1}-12, n \geq 2 \) \( a_{n}= \)