The underlying pattern for the series is (previous term * 2) + 1. Let's apply this pattern to each term: Starting with 3. (3 * 2) + 1 = 7 (7 * 2) + 1 = 15 (15 * 2) + 1 = 31 (31 * 2) + 1 = 62 + 1 = 63. However, the given term in the series is 65, not 63. If 63 were the correct term, then (63 * 2) + 1 = 126 + 1 = 127, which matches the next term in the series. Therefore, 65 is the incorrect term in the sequence. Why others are wrong: A — 7 correctly follows the pattern (3*2)+1. B — 15 correctly follows the pattern (7*2)+1. C — 31 correctly follows the pattern (15*2)+1. D — 65 does not follow the pattern; it should be 63.

The pattern alternates between multiplying by 2 and adding 1 to the preceding term. 1st term: 3 2nd term: 3 * 2 = 6 3rd term: 6 + 1 = 7 4th term: 7 * 2 = 14 (The given term is 13) 5th term: 14 + 1 = 15 (This matches the given term, continuing the correct pattern) 6th term: 15 * 2 = 30 (This matches the given term) Therefore, 13 is the wrong term; it should be 14 to maintain the sequence. Why others are wrong: A — 6 correctly follows the pattern (3 * 2). B — 7 correctly follows the pattern (6 + 1). D — 15 correctly follows the pattern (14 + 1), assuming 14 was the correct preceding term.

The pattern for this series is to add consecutive odd numbers to the preceding term. Starting with 2: 2 + 3 = 5 5 + 5 = 10 Following the pattern, the next addition should be 7: 10 + 7 = 17 However, the given term is 18, which deviates from the pattern. Continuing with the corrected term (17), the next additions are 9 and 11: 17 + 9 = 26 26 + 11 = 37 Therefore, 18 is the only term that does not follow the established pattern, as it should be 17. Why others are wrong: A — 5 follows the pattern (2 + 3). B — 10 follows the pattern (5 + 5). D — 26 follows the pattern (17 + 9), assuming the preceding term was correctly 17.

Step 1: Calculate the differences between consecutive terms in the given series. Step 2: The differences are: 6-2=4, 12-6=6, 22-12=10, 30-22=8, 42-30=12. Step 3: Observe the sequence of these differences: 4, 6, 10, 8, 12. Step 4: A consistent pattern for the differences should be an increase by 2 each time: +4, +6, +8, +10, +12. Step 5: The third difference is 10 (22-12) instead of the expected 8, and consequently, the fourth difference is 8 (30-22) instead of the expected 10. Step 6: If the term 22 were replaced by 20, the pattern of differences would be consistent: 2 (+4) = 6 6 (+6) = 12 12 (+8) = 20 (instead of 22) 20 (+10) = 30 30 (+12) = 42 Step 7: Therefore, 22 is the incorrect term in the series; it should be 20 to maintain the pattern. Why others are wrong: A — 6: This term correctly follows the pattern (2 + 4 = 6). B — 12: This term correctly follows the pattern (6 + 6 = 12). D — 30: This term correctly follows the pattern (20 + 10 = 30), assuming the preceding term is corrected to 20.

Analyze the sequence of operations between consecutive terms. From 3 to 6, the operation is +3 (3 + 3 = 6). From 6 to 18, the operation is x3 (6 x 3 = 18). From 18 to 21, the operation is +3 (18 + 3 = 21). From 21 to 63, the operation is x3 (21 x 3 = 63). From 63 to 66, the operation is +3 (63 + 3 = 66). From 66 to 198, the operation is x3 (66 x 3 = 198). The established pattern is an alternating sequence of operations: +3, then x3. Following this pattern, after 198, the next operation should be +3. So, 198 + 3 = 201. The given series has 200 as the last term, which deviates from the pattern. Why others are wrong: A — 63 correctly follows the pattern (21 x 3 = 63). B — 198 correctly follows the pattern (66 x 3 = 198). D — 21 correctly follows the pattern (18 + 3 = 21).