In the series 1, 6, 15, 28, 45, .......... the next term will be:
66
To solve this problem, we need to identify the pattern in the given series: 1, 6, 15, 28, 45, ....
Let's start by analyzing the differences between consecutive terms:
- Difference between 6 and 1: 6 - 1 = 5
- Difference between 15 and 6: 15 - 6 = 9
- Difference between 28 and 15: 28 - 15 = 13
- Difference between 45 and 28: 45 - 28 = 17
We can observe a pattern in the differences: 5, 9, 13, 17...
This sequence of differences is increasing by 4 each time (9 - 5 = 4, 13 - 9 = 4, 17 - 13 = 4). Hence, it is an arithmetic sequence with a common difference of 4.
We can find the next difference by adding 4 to the last known difference:
Next difference: 17 + 4 = 21
Now, add this next difference to the last term of the original series:
Next term: 45 + 21 = 66
Thus, the next term in the series is 66.
Option analysis:
- 66: Correct, as derived above.
- 76, 56, 84: These are not aligned with the calculated pattern/diference.
Therefore, the correct answer is 66.
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What will come in place of question mark (?) in the following number series?
2, 5, 11, 23, 44, 77, ?
What will come in place of question mark (?) in the following number series?
31, 32, 36, ?, 61, 86
What will come in the place of question mark (?) in the following number series?
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What should come in place of the question mark ‘?’ in the following number series?
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A series is given with one term wrong. Select that wrong term from the given alternatives.
J12, M24, P48, S96, U192
