Question

Which of the following is AP ?
A. 2 , 4 , 8 , 16 ....
B. $2,\dfrac{5}{2},3,\dfrac{7}{2}, \ldots $
C. -1.2 , -3.2 , -5.2 , -7.2 ....
D. -10 , -6 , -2 , 2 ....

Answer 1

Hint: To solve such a particular type of question we should use the fact that an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. Thus if there is a common difference in the consecutive terms of the series given in options then those numbers are in AP.

Complete step-by-step answer:

Checking option A ,
4-2=2
8-4=4
Hence the difference is not common , therefore not an AP .
Checking option B ,
$\dfrac{5}{2} - 2 = 3 - \dfrac{5}{2} = \dfrac{7}{2} - 3 = \dfrac{1}{2}$
$\dfrac{1}{2}$ is the common difference .
Hence it is an AP .
Checking option C ,
$ - 3.2 - \left( { - 1.2} \right) = - 5.2 - \left( { - 3.2} \right) = - 7.2 - \left( { - 5.2} \right) = 2$
2 is the common difference .
Hence it is an AP .
Checking option D ,$ - 6 - \left( { - 10} \right) = - 2 - \left( { - 6} \right) = 2 - \left( { - 2} \right) = 4$
4 is the common difference .
Hence it is an AP.

Note: These types of questions could also be done by using the formula of ${n^{th}}$ term of an AP which is ${a^n} = a + \left( {n - 1} \right)d$ . Taking the common difference as the difference of the first two consecutive, use the formula to check whether the ${n^{th}}$ term comes equal or not . But to keep it simple, we had directly subtracted the consecutive terms to check for an AP .