To determine which number will not be part of the given series, we first need to understand the pattern followed by the series. The series given is:
11, 19, 27, 35, 43, ...
Let's analyze the difference between consecutive numbers in the series:
- 19 - 11 = 8
- 27 - 19 = 8
- 35 - 27 = 8
- 43 - 35 = 8
It is evident that this is an arithmetic progression with a common difference (\(d\)) of 8. The formula for the nth term (\(a_n\)) of an arithmetic sequence is given by:
\(a_n = a + (n-1) \cdot d\)
where \(a\) is the first term, and \(d\) is the common difference. Here, \(a = 11\) and \(d = 8\).
We need to check which of the given options cannot be a term in the sequence. Plugging the nth term equation:
\(a_n = 11 + (n-1) \cdot 8\)
We solve for \(n\) to see if it results in a positive integer:
- For 434:
- For 107:
- For 307:
- For 195:
Therefore, the only option that is not a part of the series is 434.
Similar Questions
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Important Questions from Arithmetic Progression
If the arithmetic mean of a, b, c is \(\rm \frac M 3\) and \(\rm \frac{1}{a} + \frac{1}{b} = -\frac{1}{c} \) , then the arithmetic mean of a 2, b 2, c 2 is
A person saves Rs. 1000 more than he did the previous year. If he saves Rs. 2000 in the first year, in how many years will he save Rs. 170000?
How many natural numbers lie between 3 and 200 which are divisible by 7?
The arithmetic mean of 16 student's scores is 320. Find the sum of these scores.
How many three-digit numbers are divisible by 5?
