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What should come in place of ? in the given series? 6, 30, 174, ?, 6222, 37326
1038
1058
1098
1008
1038
Observe the growth rate; the series follows a pattern of multiplying by an increasing factor and adding/subtracting a changing value or using a power-based multiplier (n * multiplier + constant).
Observe the growth rate; the series follows a pattern of multiplying by an increasing factor and adding/subtracting a changing value or using a power-based multiplier (n * multiplier + constant).
Analyze the relationship between terms
Looking at the transition from 6 to 30: (6 * 5) = 30. From 30 to 174: (30 * 6) - 6 = 174. From 174 to?: (174 * 6) = 1044. Wait, let us check a more consistent pattern: (6 * 4) + 6 = 30, (30 * 5) + 24 = 174. That does not look simple. Let us try: (6 * 6) - 6 = 30; (30 * 6) - 6 = 174. This does not work. Let us try: (6 * 5) = 30; (30 * 6) - 6 = 174; (174 * 6) = 1044. Let us check the next: (1038 * 6) = 6228. Close to 6222.
Applying the pattern (n * k) - difference
The actual pattern is: (6 * 5) = 30. (30 * 6) - 6 = 174. (174 * 6) - 6 = 1038. (1038 * 6) - 6 = 6222. (6222 * 6) - 6 = 37326. The logic is multiply the previous term by 6 and subtract 6, starting from the second term.
B: 1058 does not satisfy the recursive multiplication rule; C: 1098 is arithmetically inconsistent with the subsequent term 6222; D: 1008 fails the required multiplication sequence by 6 resulting in a value far from 6222.
A is correct because the series follows the recursive formula Term(n) = (Term(n-1) * 6) - 6 starting from the second term, where 174 * 6 - 6 = 1038.
When terms in a series grow very rapidly, always test for multiplication or power-based patterns (xтБ┐ or x*n) instead of simple addition.
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