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
- If the ratio of the 11th term of an AP to its 18th term is 2 : 3, find the ratio of the sum of its first five terms to the sum of its first 10 terms.
- If the sum of five consecutive multiples of 2 is 660, then find the largest number.
- The $10^{\text{th}}$ term of the Arithmetic Progression $2, 7, 12, \dots$ is:
- The sum of the first 12 multiples of 6 is:
- What is the $50^{\text{th}}$ term of Arithmetic Progression 3, 8, 13, 18, 23, ........?
- The sum of all odd numbers between 0 and 52 is:
- The tenth term of the sequence 2, 5, 8, 11, ......will be:
- What is the sum of the first 12 multiples of 4?
- What is the sum of the squares of all two-digit numbers each of which is completely divisible by 4?
- What is the sum of the first 25 odd numbers?
Important Questions from Arithmetic Progression
If the nth term of a sequence is \(\frac{2 n+5}{7}\), then what is the sum of its first 140 terms?
What is the arithmetic mean of first 8 multiples of 13?
The average of five consecutive odd natural numbers is 27. The product of the first and fifth number is:
Find the sum of all the numbers between 100 to 200 which are divisible by 12.
In a garden, there are 6 daisy plants the first year. Each year, a gardener adds 3 new daisy plants the first year and loses 2 each year. He has 26 jasmine plants the first year and loses 2 each year. When will the number of daisy plants equal the number of jasmine plants after the first year?
