Which of the following number is in the list of numbers 5, 11, 17, 23, ... ?

The correct answer is (A) 179.

Arithmetic progression verification:

• Given sequence: $5, 11, 17, 23,$$\dots$ (Arithmetic Progression).
• First term ($a$) = 5, Common difference ($d$) = $11 - 5 = 6$.
• The general $n$-th term is: $T_n = a + (n - 1)d = 5 + (n - 1)6 = 6n - 1$.
• Setting $6n - 1 =$$\text{Number}$ $\implies$ 6n = $\text{Number}$ + 1 (must be divisible by 6).
• Testing option (A): $179 + 1 = 180$$\implies$ n = $\frac{180}{6}$ = 30 (Valid integer term).
• Other options ($189+1=190$, $169+1=170$, $159+1=160$) are not divisible by 6.
• Thus, 179 is the 30th term in the sequence.