Adding 1 to both sides yields n = 16. Therefore, the 16^(th) term of the given progression is 78.

which time of Ap 3,8,13,18 is 78

Answer: The $16^{\text{th}}$ term of the given AP is $78$ .

Step-by-step solution

Step 1: Identify the first term, common difference, and nth term

From the given arithmetic progression $3, 8, 13, 18, \dots$ , we identify the first term $a = 3$ . The common difference is found by subtracting the first term from the second term, giving $d = 8 - 3 = 5$ . We let the $n^{\text{th}}$ term be $a_n = 78$ .

Step 2: State the formula for the nth term and substitute known values

We recall the formula for the $n^{\text{th}}$ term of an arithmetic progression, which is $a_n = a + (n - 1)d$ . Substituting $a = 3$ , $d = 5$ , and $a_n = 78$ into the formula gives $78 = 3 + (n - 1) \times 5$ .

Step 3: Solve the linear equation for n

Subtracting $3$ from both sides gives $75 = 5(n - 1)$ . Dividing both sides by $5$ gives $n - 1 = 15$ .

Step 4: Determine the value of n

Adding $1$ to both sides yields $n = 16$ . Therefore, the $16^{\text{th}}$ term of the given progression is $78$ .

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