Question

How many terms are there in the A.P. \( 7, 13, 19, \dots \), 205?

• A. 33
• B. 32
• C. 35
• D. 34

Hint:

To find the number of terms in an A.P., use the formula for the nth term and solve for \( n \) when the last term is given.

Answer 1

The Correct Option is D

The first term of the A.P. is \( a = 7 \), and the common difference is \( d = 6 \). The general formula for the nth term of an A.P. is: \[ T_n = a + (n - 1)d \] Step 1: We are given that the last term is 205, so: \[ 205 = 7 + (n - 1) \times 6 \] Step 2: Simplify the equation: \[ 205 - 7 = (n - 1) \times 6 \] \[ 198 = (n - 1) \times 6 \] \[ n - 1 = \frac{198}{6} = 33 \] \[ n = 34 \] Thus, the number of terms in the A.P. is 34.