Select the number from among the given options that will come next in the following series. $20, 40, 63, 90, 122,$ _____
Number Series Analysis
The task is to find the next number in the given numerical sequence: 20, 40, 63, 90, 122.
Calculating Differences Between Terms
We examine the differences between consecutive numbers in the series to find a pattern.
- Difference between the 1st and 2nd term: $40 - 20 = 20$
- Difference between the 2nd and 3rd term: $63 - 40 = 23$
- Difference between the 3rd and 4th term: $90 - 63 = 27$
- Difference between the 4th and 5th term: $122 - 90 = 32$
The sequence of first differences is: 20, 23, 27, 32.
Calculating Second Differences
Now, we find the differences between the terms in the first difference sequence.
- Difference between the 1st and 2nd difference: $23 - 20 = 3$
- Difference between the 2nd and 3rd difference: $27 - 23 = 4$
- Difference between the 3rd and 4th difference: $32 - 27 = 5$
The sequence of second differences is: 3, 4, 5.
Identifying the Pattern Progression
The second differences (3, 4, 5) show a clear pattern of increasing by 1 for each step. Therefore, the next second difference is expected to be $5 + 1 = 6$.
Determining the Next First Difference
To find the next difference in the original series, we add the predicted next second difference (6) to the last calculated first difference (32).
Next first difference = $32 + 6 = 38$.
Calculating the Next Term in the Series
Finally, we find the next term in the original series by adding this next first difference (38) to the last term of the series (122).
Next term = $122 + 38 = 160$.
The pattern suggests the next term should be 160.
Provided Options and Answer
The given options are:
- $120$
- $150$
- $160$
- $110$
The correct answer provided is Option B: $150$.
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BAC, QRP, EDF, TUS, _____.
Important Questions from Series
Select the option figure in which the given figure (X) is embedded (rotation is NOT allowed).
Identify the figure given in the options which when put in place of ? will logically complete the series.
When is a series of terms said to be in the order of increasing extension?
(A) When each term in the series (except the first) denotes a class having more members than a class denoted by the term preceding it.
(B) When the class size gets larger with each successive term.
(C) When each term in the series (except the first) denotes a class having fewer members than the class denoted by the term preceding it.
(D) When the class size gets smaller with each successive term
Choose the most appropriate answer from the options given below :
In the following question, select the missing number from the given series.
5, 10, 17, 26, 37, ?, 65
In the following question, select the missing number from the given series.
5, 10, 17, 26, 37, ?, 65
