Question

Check whether 301 is a term of the sequence \( 5, 11, 17, 23, \dots \).

Hint:

To check if a number is a term of an A.P., substitute the number into the general term formula \( a_n = a + (n-1)d \). If \( n \) is not an integer, the number is not a term of the A.P.

Answer 1

Given A.P.:
\[ a = 5, \quad d = 11 - 5 = 6 \] General term:
\[ a_n = a + (n-1)d \] \[ 301 = 5 + (n-1)6 \] \[ 301 - 5 = (n-1)6 \] \[ 296 = (n-1)6 \] \[ n-1 = \frac{296}{6} = 49.33 \] Since \( n \) is not an integer, 301 is not a term.
Correct Answer: \( 301 \text{ is not a term of the A.P.} \)