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.
Important Questions from Progression (Notes)
- The sum of 16 terms of the series $\sqrt{2} + \sqrt{8} + \sqrt{18} + \sqrt{32} + .....$ is :
- A pilgrim starts walking for a journey of 115 km. On the first day he covers 7 km, the next day 9 km, and likewise keeps adding 2 km everyday till he reaches 15 km per day which he maintains for the rest of the journey. How many days in all will he take to complete the journey?
If a, b and c are in Geometric Progression and $a^\frac{1}{x} = b^\frac{1}{y} = c^\frac{1}{z}$ then, x, y, z are in ________.
Which of the following statement is true about the geometric series
$ 1 + r +r^2 + r^3 + ...............; (r > 0) $?
$6240$ रुपये की राशि $30$ किस्तों में इस प्रकार चुकाई जाती है कि प्रत्येक किस्त पिछली किस्त से $10$ रुपये अधिक है । पहली किस्त की मूल्य ____________है।
