diff --git a/src/bin/1.rs b/src/bin/1.rs
index b9d5945..49f7114 100644
--- a/src/bin/1.rs
+++ b/src/bin/1.rs
@@ -1,23 +1,60 @@
 /// Problem 1
 ///
-/// If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
+/// If we list all the natural numbers below 10 that are multiples of 3 or 5, 
+/// we get 3, 5, 6 and 9. The sum of these multiples is 23.
 ///
 /// Find the sum of all the multiples of 3 or 5 below 1000.
 
-fn sum_multiples_3_5(n: i32) -> i32 {
+fn problem_1_sol_1(n: i32) -> i32 {
     let sum = (0..n).filter(|x| x % 3 == 0 || x % 5 == 0).sum();
 
     sum
 }
 
-fn main() {
-    println!("the sum of all the multiples of 3 or 5 below 10: {}", sum_multiples_3_5(10));
-    println!("the sum of all the multiples of 3 or 5 below 1000: {}", sum_multiples_3_5(1000));
+/// Calculates and returns the sum of multiples of a `num`
+/// below the `limit` using arithmetic series
+fn sum_multiples(num: i32, limit: i32) -> i32 {
+    let num_of_multiples = (limit - 1) / num;
+    num * ((num_of_multiples * (num_of_multiples + 1)) / 2)
+}
+
+/// Calculates and returns the sum of all the multiples of 3 or 5 below 1000.
+/// using the helper function ```sum_multiples```
+pub fn problem_1_sol_2(limit: i32) -> i32 {
+    let sum_3 = sum_multiples(3, limit);
+    let sum_5 = sum_multiples(5, limit);
+    let sum_15 = sum_multiples(15, limit);
+    sum_3 + sum_5 - sum_15
 }
 
+fn main() {
+    println!(
+        "the sum of all the multiples of 3 or 5 below 10: {}",
+        problem_1_sol_1(10)
+    );
+    println!(
+        "the sum of all the multiples of 3 or 5 below 1000: {}",
+        problem_1_sol_1(1000)
+    );
+    print!("Using problem_1_sol_2:");
+    print!(
+        "\tthe sum of all the multiples of 3 or 5 below 1000: {}",
+        problem_1_sol_2(1000)
+    );
+}
 
 #[test]
 fn test() {
-    assert_eq!(sum_multiples_3_5(10), 23);
-    assert_eq!(sum_multiples_3_5(1000), 233168);
+    assert_eq!(problem_1_sol_1(10), 23);
+    assert_eq!(problem_1_sol_1(1000), 233168);
+}
+
+#[test]
+fn sum_of_multiples_3_below_10() {
+    assert_eq!(18, sum_multiples(3, 10));
+}
+
+#[test]
+fn test_sum_below_10() {
+    assert_eq!(23, problem_1_sol_2(10));
 }