Question

find the 78th term of the arithmetic sequence 14, 5, -4, ...

Explanation:

Step1: Recall the formula for the nth term of an arithmetic sequence

The formula for the nth term of an arithmetic sequence is $a_n = a_1 + (n - 1)d$, where $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference.

Step2: Identify $a_1$, $d$, and $n$

• $a_1 = 14$ (the first term of the sequence)
• To find $d$, subtract the first term from the second term: $d = 5 - 14 = -9$
• $n = 78$ (we want the 78th term)

Step3: Substitute the values into the formula

$a_{78} = 14 + (78 - 1)(-9)$
First, calculate $78 - 1 = 77$
Then, calculate $77 \times (-9) = -693$
Finally, calculate $14 + (-693) = 14 - 693 = -679$

Answer:

-679