To find the 78th term of the arithmetic sequence 14, 5, -4, ..., we use the formula for the $n$th term of an arithmetic sequence:

$a_n = a_1 + (n - 1) d$

where:

• $a_1 = 14$ (first term),
• $d$ is the common difference,
• $n = 78$ (term to find).

Step 1: Find the Common Difference

The common difference $d$ is given by:

$d = a_2 - a_1 = 5 - 14 = -9$

Step 2: Find $a_{78}$

$a_{78} = 14 + (78 - 1)(-9)$

$= 14 + 77(-9)$

$= 14 - 693$

$= -679$

Thus, the 78th term of the sequence is -679.

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Related Questions:

1. What is the sum of the first 78 terms of this sequence?
2. What is the general formula for the $n$th term of this sequence?
3. Which term of the sequence is equal to -500?
4. How many terms of the sequence are needed to reach a negative sum?
5. What is the 100th term of this sequence?

Math Tip:

In an arithmetic sequence, the common difference $d$ determines whether the sequence increases or decreases. If $d$ is negative, the sequence decreases over time!