Question

1. given -15, -9, -3, + 3... 45

a) determine ( t_n )

Explanation:

Step1: Identify Sequence Type

The sequence is -15, -9, -3, 3, ..., 45. Check the common difference: $-9 - (-15) = 6$, $-3 - (-9) = 6$, $3 - (-3) = 6$. So it's an arithmetic sequence with first term $a_1 = -15$, common difference $d = 6$, and last term $a_n = 45$.

Step2: Use Arithmetic Sequence Formula

The formula for the $n$th term of an arithmetic sequence is $a_n = a_1 + (n - 1)d$. Substitute $a_n = 45$, $a_1 = -15$, $d = 6$:
$45 = -15 + (n - 1) \times 6$

Step3: Solve for n

Add 15 to both sides: $60 = (n - 1) \times 6$
Divide both sides by 6: $10 = n - 1$
Add 1 to both sides: $n = 11$

Answer:

The value of \( n \) is 11.