Below given are two series I and II. In series I, 'm' is the correct term and in series II, 'n' is the wrong term.
Series I: 20, 30, 60, 150, 525, 1575
Series II: 12, 20, 47, 111, 250, 452
Find the value of (3m - 4n).
Answer (2)
The value of (3m - 4n) is calculated by determining m from Series I, which is 1575, and n from Series II, which is 452. Upon substituting these values into the expression, we find that (3m - 4n) equals 2917. Thus, the final value is 2917.
;
To solve this problem, we need to first analyze both series separately to determine the correct term m in Series I and the incorrect term n in Series II.
Series I : 20, 30, 60, 150, 525, 1575
Let's look for a pattern:
20 to 30: Increase by 10.
30 to 60: Increase by 30.
60 to 150: Increase by 90.
150 to 525: Increase by 375.
525 to 1575: Increase by 1050.
This sequence can be seen as multiplying previous terms by increasing numbers. Let's verify:
20 to 30: 20 × 1.5 = 30
30 to 60: 30 × 2 = 60
60 to 150: 60 × 2.5 = 150
150 to 525: 150 × 3.5 = 525
525 to 1575: 525 × 3 = 1575 (Correction: It's indeed 525 × 3 = 1575 )
Here, the correct term according to the series is m = 150 .
Series II : 12, 20, 47, 111, 250, 452
Let's identify the pattern and look for any inconsistencies.
12 to 20: Increase by 8.
20 to 47: Increase by 27.
47 to 111: Increase by 64.
111 to 250: Increase by 139.
250 to 452: Increase by 202.
The differences between the numbers follow a pattern of approximate increments, but if you look closely, they don't follow a consistent pattern like squares or cubes. Calculating by trial can help.
We'll find the discrepancy in changes added:
Difference missing for the original 3rd position: 20 + ( 30 + 1 ) = 48 not 47.
Thus, n = 47 is the incorrect term in Series II.
Finally, the task is to find 3 m − 4 n :
3 m = 3 × 150 = 450
4 n = 4 × 47 = 188
3 m − 4 n = 450 − 188 = 262
Therefore, the value of 3 m − 4 n is 262 .
