Find the 15th term of the AP 3, 8, 13,

Answer: $73$

Step-by-step solution

Step 1: Identify the first term and common difference

From the given arithmetic progression $3, 8, 13, \dots$ , the first term $a$ is $3$ . The common difference $d$ is obtained by subtracting the first term from the second term: $8 - 3 = 5$ .

Step 2: State the formula for the nth term of an AP

The standard formula for the $n^{\text{th}}$ term of an arithmetic progression is $a_n = a + (n - 1)d$ , where $n$ represents the position of the term.

Step 3: Substitute the values to find the 15th term

We substitute $a = 3$ , $d = 5$ , and $n = 15$ into the $n^{\text{th}}$ term formula. Multiplying $14$ by $5$ gives $70$ .

Step 4: Compute the final result

Adding $3$ and $70$ gives $73$ . Thus, the 15th term of the arithmetic progression is $73$ .

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