The term number n must be a positive integer. Since (79)/(6) is not a natural number, 78 cannot be a term of the given AP.

is 78 atom of the AP 5 11 17 23

Answer: No, 78 is not a term of the AP $5, 11, 17, 23, \ldots$

Step-by-step solution

Step 1: Identify the first term and common difference

From the given Arithmetic Progression $5, 11, 17, 23, \ldots$ , the first term is $a = 5$ . We find the common difference by subtracting the first term from the second term, giving $d = 11 - 5 = 6$ .

Step 2: Set up the equation for the $n$ -th term

Assume that 78 is the $n$ -th term of this AP, so $a_n = 78$ . We substitute $a = 5$ and $d = 6$ into the general formula $a_n = a + (n - 1)d$ .

Step 3: Solve for $n$

Expanding the equation gives $78 = 6n - 1$ . Adding 1 to both sides gives $6n = 79$ , which leads to $n = \frac{79}{6}$ .

Step 4: Conclude whether 78 is a term

The term number $n$ must be a positive integer. Since $\frac{79}{6}$ is not a natural number, 78 cannot be a term of the given AP.

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