Chapter: Arithmetic Progression· Mathematics Part 1 (Algebra)
Answer: 70,821
The smallest three-digit number of the form \(7k + 3\): \(7 \times 14 + 3 = 101\). The largest: \(7 \times 142 + 3 = 997\).
So the numbers are 101, 108, 115, …, 997: an A.P. with \(a = 101\), \(d = 7\), \(t_n = 997\).
\(997 = 101 + (n - 1) \times 7 \Rightarrow 896 = 7(n - 1) \Rightarrow n - 1 = 128 \Rightarrow n = 129\)
\(S_{129} = \dfrac{129}{2}(101 + 997) = \dfrac{129}{2} \times 1098 = 129 \times 549 = 70821\)