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
• B. 216
• C. 218
• D. 219

Answer 1

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।