Explanation

(b)
Let the three numbers $(a - d),a$ and $(a + d)$ are in AP. Then,
$(a - d) + a + (a + d) = 18\ \ \ \Rightarrow a = 6$ …(i)
and $(a - d)^{2} + a^{2} + (a + d)^{2} = 158$
$\Rightarrow 3a^{2} + 2d^{2} = 158$
$\Rightarrow 2d^{2} = 158 - 3 \times 36$ [from Eq. (i)]
$\Rightarrow \ d = \pm 5$
Hence, the required numbers are 1, 6, 11 or 11, 6, 1
Thus, greatest number is 11.