7, 19, 31, 43, ...
To determine the common difference of an Arithmetic Progression (A.P.) series, we use the formula for the common difference \(d\) of an A.P., which is given by subtracting the first term from the second term, i.e., \(d = a_2 - a_1\).
Given the series: 7, 19, 31, 43, ...
- The first term (\(a_1\)) is 7.
- The second term (\(a_2\)) is 19.
Now, calculate the common difference \(d\):
Using the formula\(d = a_2 - a_1\), we substitute the known values:
\(d = 19 - 7\)
This simplifies to:
\(d = 12\)
Therefore, the common difference of the given A.P. series is 12.
Looking at the options provided:
- Option 1: 19
- Option 2: 5
- Option 3: 12 (Correct Option)
- Option 4: 7
The correct answer, as calculated, is indeed 12. Thus, Option 3 is correct.
This common difference confirms that each term in the sequence after the first is obtained by adding 12 to the previous term, verifying the series is indeed an Arithmetic Progression.
Similar Questions
- What would be the $178^{\text{th}}$ term in the following series?
2, 5, 8, 11, 14, ... - The $5^{\text{th}}$ and the $17^{\text{th}}$ terms of an A. P. series are 52 and 184 respectively. Find the common difference of the series.
Important Questions from Progression (Notes)
- The sum of 16 terms of the series $\sqrt{2} + \sqrt{8} + \sqrt{18} + \sqrt{32} + .....$ is :
- An auditorium has 8 seats in the first row, with every row to follow having 4 more seats than its preceding row. The total capacity is 416. What is the minimum number of rows needed to seat 150 people?
- The $5^{\text{th}}$ and $9^{\text{th}}$ terms of an arithmetic progression are 7 and 13 respectively. What is the $15^{\text{th}}$ term?
- Find the sum of the G.P.:
$5/11, 5/121, 5/1331, 5/14641, ...$ to $n$ terms. Suppose $a_1, a_2,..., a_{300}$ are integers such that $a_{i-1}+ a_i+ a_{i+1} = 2025$ for all $i = 2,3, ..., 299$.
If $a_7 = -5, a_9 = 37$, then the value of $a_{106}$ is
