What is the value of X in the sequence
20, 10, 10, 15, 30, 75, X?
UPSC-2022
The problem asks us to find the next term in a given sequence. We need to identify the pattern or rule governing the sequence by examining the relationship between consecutive terms.
D) 225 is the correct answer because the pattern of multiplying factors between consecutive terms is an arithmetic progression (0.5, 1, 1.5, 2, 2.5, ...). The next factor is 3, so \(75 \times 3 = 225\).
What is X in the sequence
132, 129, 124, 117, 106, 93, X?
UPSC-2019
The problem asks us to find the next term in a given sequence of numbers. We need to identify the pattern or rule governing the sequence by calculating the differences between consecutive terms. This will help us predict the next difference and, consequently, the next term.
C) 76 — The pattern of differences between consecutive terms is a sequence of prime numbers (3, 5, 7, 11, 13). The next prime number is 17. Subtracting 17 from 93 gives 76.
What is X in the sequence
4, 196, 16, 144, 36, 100, 64, X?
UPSC-2019
The given sequence is an alternating series. We need to identify two separate patterns within the sequence: one for the odd-positioned terms and another for the even-positioned terms. By finding the pattern for the even-positioned terms, we can determine the value of X.
Let's look at the terms at odd positions (1st, 3rd, 5th, 7th):
\[ 4, 16, 36, 64 \]Let's look at the terms at even positions (2nd, 4th, 6th, 8th):
\[ 196, 144, 100, \text{X} \]The terms are:
This sub-sequence consists of squares of consecutive even numbers (2, 4, 6, 8, ...).
The terms are:
This sub-sequence consists of squares of consecutive even numbers, decreasing by 2 each time (14, 12, 10, ...).
Following the pattern of decreasing even numbers, the next number after 10 would be \(10 - 2 = 8\).
Therefore, X will be the square of 8.
\[ \text{X} = 8^2 = 64 \]B) 64 is the correct answer because the even-positioned terms form a sequence of squares of decreasing even numbers: \(14^2, 12^2, 10^2, 8^2\).
What is the value of 'X' in the question
2,7, 22, 67, 202, X,….. 1822?
UPSC-2021
The problem presents a number series and asks for the value of 'X' which is a missing term in the sequence. To solve this, we need to identify the pattern or rule governing the series.
C) 607 is the correct value for X, as determined by the pattern of multiplying the previous difference by 3.
Consider the sequence given below:
4/12/95, 1/1/96, 29/1/96, 26/2/96, …....
What is the next term of the series?
UPSC-2018
This problem involves identifying a pattern in a sequence of dates. We need to calculate the number of days between consecutive terms to find the rule governing the sequence and then apply it to find the next term.
B) 25/3/96. This is derived by adding 28 days to the last given term, 26/2/96, following the established pattern.
Select the number from among the given options that can replace the question mark ? In the following series
3, 12, 27, 48, 75, 108, ?
To find the missing number in the series, we need to identify the pattern or rule governing the sequence of numbers. We will analyze the relationship between consecutive terms or the terms themselves.
Since the second-order difference is constant (6), this indicates a quadratic pattern or a pattern where the differences increase by a constant amount.
Both methods yield the same result.
Correct Option: A) 147
