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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Important Questions from Number Series
- In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 676 :: 17 : Y - Which of the following options should come in place of the question mark (?) in the given series to make it logically complete?
125, 128, 133, 140, 149,? - What should come in place of the question mark (?) in the given series?
801 800 792 765 701 ? - What should come in place of the question mark (?) in the given series?
101 110 121 134 149 ? - What should come in place of the question mark (?) in the given series?
40, 48, 58, 66, 76, ?
