Question

How many terms are in the A.P. 3, 8, 13, 18, ..., 93 ?

• A. \( 19 \)
• B. \( 18 \)
• C. \( 20 \)
• D. \( 16 \)

Hint:

To find the number of terms in an A.P., use: \[ n = \frac{(a_n - a)}{d} + 1. \]

Answer 1

The Correct Option is A

Given A.P.:
\[ 3, 8, 13, 18, \dots, 93 \] First term: \( a = 3 \), Common difference: \( d = 8 - 3 = 5 \).
Using the general formula: \[ a_n = a + (n-1) d \] Setting \( a_n = 93 \): \[ 93 = 3 + (n-1)(5) \] \[ 93 - 3 = (n-1) \times 5 \] \[ 90 = (n-1) \times 5 \] \[ n-1 = \frac{90}{5} = 18 \] \[ n = \]