Find the sum of the A.P.; 14, 21, 28, ……., 168.

Let 168 be n^th term.

⇒ a_n = a + (n - 1)d

⇒ 168 = 14 + (n - 1)7

⇒ 168 = 14 + 7n - 7

⇒ 168 = 7n + 7

⇒ 161 = 7n

⇒ n = 23.

$S = \dfrac{n}{2}(a + l) \\[1em] = \dfrac{23}{2}(14 + 168) \\[1em] = \dfrac{23}{2} \times 182 \\[1em] = 23 \times 91 \\[1em] = 2093.$

Hence, n = 23 and sum = 2093.