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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