diff --git a/src/main/java/com/thealgorithms/maths/LucasSeries.java b/src/main/java/com/thealgorithms/maths/LucasSeries.java
index e277c511f317..90a35f0d6259 100644
--- a/src/main/java/com/thealgorithms/maths/LucasSeries.java
+++ b/src/main/java/com/thealgorithms/maths/LucasSeries.java
@@ -1,38 +1,69 @@
 package com.thealgorithms.maths;
 
 /**
- * https://en.wikipedia.org/wiki/Lucas_number
+ * Utility class for calculating Lucas numbers.
+ * The Lucas sequence is similar to the Fibonacci sequence but starts with 2 and
+ * 1.
+ * The sequence follows: L(n) = L(n-1) + L(n-2)
+ * Starting values: L(1) = 2, L(2) = 1
+ * Sequence: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, ...
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Lucas_number">Lucas Number</a>
+ * @author TheAlgorithms Contributors
  */
 public final class LucasSeries {
     private LucasSeries() {
     }
 
     /**
-     * Calculate nth number of Lucas Series(2, 1, 3, 4, 7, 11, 18, 29, 47, 76,
-     * 123, ....) using recursion
+     * Calculate the nth Lucas number using recursion.
+     * Time Complexity: O(2^n) - exponential due to recursive calls
+     * Space Complexity: O(n) - recursion depth
      *
-     * @param n nth
-     * @return nth number of Lucas Series
+     * @param n the position in the Lucas sequence (1-indexed, must be positive)
+     * @return the nth Lucas number
+     * @throws IllegalArgumentException if n is less than 1
      */
     public static int lucasSeries(int n) {
-        return n == 1 ? 2 : n == 2 ? 1 : lucasSeries(n - 1) + lucasSeries(n - 2);
+        if (n < 1) {
+            throw new IllegalArgumentException("Input must be a positive integer. Provided: " + n);
+        }
+        if (n == 1) {
+            return 2;
+        }
+        if (n == 2) {
+            return 1;
+        }
+        return lucasSeries(n - 1) + lucasSeries(n - 2);
     }
 
     /**
-     * Calculate nth number of Lucas Series(2, 1, 3, 4, 7, 11, 18, 29, 47, 76,
-     * 123, ....) using iteration
+     * Calculate the nth Lucas number using iteration.
+     * Time Complexity: O(n) - single loop through n iterations
+     * Space Complexity: O(1) - constant space usage
      *
-     * @param n nth
-     * @return nth number of lucas series
+     * @param n the position in the Lucas sequence (1-indexed, must be positive)
+     * @return the nth Lucas number
+     * @throws IllegalArgumentException if n is less than 1
      */
     public static int lucasSeriesIteration(int n) {
+        if (n < 1) {
+            throw new IllegalArgumentException("Input must be a positive integer. Provided: " + n);
+        }
+        if (n == 1) {
+            return 2;
+        }
+        if (n == 2) {
+            return 1;
+        }
+
         int previous = 2;
         int current = 1;
-        for (int i = 1; i < n; i++) {
+        for (int i = 2; i < n; i++) {
             int next = previous + current;
             previous = current;
             current = next;
         }
-        return previous;
+        return current;
     }
 }
diff --git a/src/test/java/com/thealgorithms/maths/LucasSeriesTest.java b/src/test/java/com/thealgorithms/maths/LucasSeriesTest.java
index 3576268c5d0c..4b6c1e41ecb6 100644
--- a/src/test/java/com/thealgorithms/maths/LucasSeriesTest.java
+++ b/src/test/java/com/thealgorithms/maths/LucasSeriesTest.java
@@ -1,28 +1,158 @@
 package com.thealgorithms.maths;
 
 import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
 
 import org.junit.jupiter.api.Test;
 
-public class LucasSeriesTest {
+/**
+ * Test cases for {@link LucasSeries} class.
+ * Tests both recursive and iterative implementations for correctness,
+ * edge cases, and error handling.
+ */
+class LucasSeriesTest {
+
+    /**
+     * Test the first Lucas number L(1) = 2
+     */
     @Test
-    void lucasSeriesTwo() {
+    void testFirstLucasNumber() {
         assertEquals(2, LucasSeries.lucasSeries(1));
         assertEquals(2, LucasSeries.lucasSeriesIteration(1));
     }
+
+    /**
+     * Test the second Lucas number L(2) = 1
+     */
     @Test
-    void lucasSeriesOne() {
+    void testSecondLucasNumber() {
         assertEquals(1, LucasSeries.lucasSeries(2));
         assertEquals(1, LucasSeries.lucasSeriesIteration(2));
     }
+
+    /**
+     * Test the third Lucas number L(3) = 3
+     */
+    @Test
+    void testThirdLucasNumber() {
+        assertEquals(3, LucasSeries.lucasSeries(3));
+        assertEquals(3, LucasSeries.lucasSeriesIteration(3));
+    }
+
+    /**
+     * Test the fourth Lucas number L(4) = 4
+     */
     @Test
-    void lucasSeriesSeven() {
+    void testFourthLucasNumber() {
+        assertEquals(4, LucasSeries.lucasSeries(4));
+        assertEquals(4, LucasSeries.lucasSeriesIteration(4));
+    }
+
+    /**
+     * Test the fifth Lucas number L(5) = 7
+     */
+    @Test
+    void testFifthLucasNumber() {
         assertEquals(7, LucasSeries.lucasSeries(5));
         assertEquals(7, LucasSeries.lucasSeriesIteration(5));
     }
+
+    /**
+     * Test the sixth Lucas number L(6) = 11
+     */
+    @Test
+    void testSixthLucasNumber() {
+        assertEquals(11, LucasSeries.lucasSeries(6));
+        assertEquals(11, LucasSeries.lucasSeriesIteration(6));
+    }
+
+    /**
+     * Test the seventh Lucas number L(7) = 18
+     */
+    @Test
+    void testSeventhLucasNumber() {
+        assertEquals(18, LucasSeries.lucasSeries(7));
+        assertEquals(18, LucasSeries.lucasSeriesIteration(7));
+    }
+
+    /**
+     * Test the eighth Lucas number L(8) = 29
+     */
+    @Test
+    void testEighthLucasNumber() {
+        assertEquals(29, LucasSeries.lucasSeries(8));
+        assertEquals(29, LucasSeries.lucasSeriesIteration(8));
+    }
+
+    /**
+     * Test the ninth Lucas number L(9) = 47
+     */
     @Test
-    void lucasSeriesEleven() {
+    void testNinthLucasNumber() {
+        assertEquals(47, LucasSeries.lucasSeries(9));
+        assertEquals(47, LucasSeries.lucasSeriesIteration(9));
+    }
+
+    /**
+     * Test the tenth Lucas number L(10) = 76
+     */
+    @Test
+    void testTenthLucasNumber() {
+        assertEquals(76, LucasSeries.lucasSeries(10));
+        assertEquals(76, LucasSeries.lucasSeriesIteration(10));
+    }
+
+    /**
+     * Test the eleventh Lucas number L(11) = 123
+     */
+    @Test
+    void testEleventhLucasNumber() {
         assertEquals(123, LucasSeries.lucasSeries(11));
         assertEquals(123, LucasSeries.lucasSeriesIteration(11));
     }
+
+    /**
+     * Test larger Lucas numbers to ensure correctness
+     */
+    @Test
+    void testLargerLucasNumbers() {
+        assertEquals(199, LucasSeries.lucasSeries(12));
+        assertEquals(199, LucasSeries.lucasSeriesIteration(12));
+        assertEquals(322, LucasSeries.lucasSeries(13));
+        assertEquals(322, LucasSeries.lucasSeriesIteration(13));
+        assertEquals(521, LucasSeries.lucasSeries(14));
+        assertEquals(521, LucasSeries.lucasSeriesIteration(14));
+        assertEquals(843, LucasSeries.lucasSeries(15));
+        assertEquals(843, LucasSeries.lucasSeriesIteration(15));
+    }
+
+    /**
+     * Test that both methods produce the same results
+     */
+    @Test
+    void testRecursiveAndIterativeConsistency() {
+        for (int i = 1; i <= 15; i++) {
+            assertEquals(LucasSeries.lucasSeries(i), LucasSeries.lucasSeriesIteration(i), "Mismatch at position " + i);
+        }
+    }
+
+    /**
+     * Test invalid input: zero
+     */
+    @Test
+    void testZeroInputThrowsException() {
+        assertThrows(IllegalArgumentException.class, () -> LucasSeries.lucasSeries(0));
+        assertThrows(IllegalArgumentException.class, () -> LucasSeries.lucasSeriesIteration(0));
+    }
+
+    /**
+     * Test invalid input: negative number
+     */
+    @Test
+    void testNegativeInputThrowsException() {
+        assertThrows(IllegalArgumentException.class, () -> LucasSeries.lucasSeries(-1));
+        assertThrows(IllegalArgumentException.class, () -> LucasSeries.lucasSeriesIteration(-1));
+        assertThrows(IllegalArgumentException.class, () -> LucasSeries.lucasSeries(-5));
+        assertThrows(IllegalArgumentException.class, () -> LucasSeries.lucasSeriesIteration(-5));
+    }
 }