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Question

# Q70. Find the next number in the given number series: 1, 2, 9, 28, 65, 126, ? दी गई संख्या श्रृंखला में अगली संख्या ज्ञात कीजिए? 1, 2, 9, 28, 65, 126, ?

A

217

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B

216

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C

218

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D

219

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Solution

## The correct option is A 217 The original series is: 1, 2, 9, 28, 65, 126, ? We can see that the elements in the above series are in the following format: N3 + 1, where N = position of the element in the series, starting from 0. Thus, the first element = 03 + 1 = 0 + 1 = 1 Second element = 13 + 1 = 1 + 1 = 2 Third element = 23 + 1 = 8 + 1 = 9 Fourth element = 33 + 1 = 27 + 1 = 28 Fifth element = 43 + 1 = 64 + 1 = 65 Sixth element = 53 + 1 = 125 + 1 = 126 Thus, the seventh element = 63 + 1 = 216 + 1 = 217 Hence, 217 is the required answer. वास्तिक श्रेणी हैः 1, 2, 9, 28, 65, 126, ? हम देख सकते हैं कि उपर्युक्त श्रेणी में अवयव निम्नलिखित प्रारूप में हैं: N3 + 1, जहां N = 0 से आंरभ होकर श्रेणी में अवयवों की स्थिति। इस प्रकार, पहला अवयव = 03 + 1 = 0 + 1 = 1 दूसरा अवयव = 13 + 1 = 1 + 1 = 2 तीसरा अवयव = 23 + 1 = 8 + 1 = 9 चौथा अवयव = 33 + 1 = 27 + 1 = 28 पांचवां अवयव = 43 + 1 = 64 + 1 = 65 छठवां अवयव = 53 + 1 = 125 + 1 = 126 इस प्रकार, सातवां अवयव = 63 + 1 = 216 + 1 = 217 अतः, 217 वांछित उत्तर है।

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