Subtract 7 from both sides to get (n - 1) × 6 = 198. Next, divide by 6 to find n - 1 = 33. Adding 1 to both sides gives n = 34.

find the number of terms in the AP 7 13 19......205

Answer: The number of terms in the given AP is 34.

Step-by-step solution

Step 1: Identify the parameters of the AP

From the given arithmetic progression, the first term $a$ is $7$ . The common difference $d$ is found by subtracting the first term from the second term: $13 - 7 = 6$ . The last term of this finite sequence is $a_n = 205$ .

Step 2: State the formula for the nth term

We use the standard formula for the $n$ -th term of an arithmetic progression, which relates the $n$ -th term $a_n$ to the first term $a$ , the number of terms $n$ , and the common difference $d$ .

Step 3: Substitute the values into the formula

Substitute $a = 7$ , $d = 6$ , and $a_n = 205$ directly into the $n$ -th term formula.

Step 4: Solve for n

Subtract $7$ from both sides to get $(n - 1) \times 6 = 198$ . Next, divide by $6$ to find $n - 1 = 33$ . Adding $1$ to both sides gives $n = 34$ .

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