Question:

If an denotes the nth term of the AP 2, 7, 12, 17, ... , find the value of (a30 − a20).

Solution:

The given AP is 2, 7, 12, 17, ... .

Here, a = 2 and d = 7 − 2 = 5

$\therefore a_{30}-a_{20}$

$=[2+(30-1) \times 5]-[2+(20-1) \times 5] \quad\left[a_{n}=a+(n-1) d\right]$

$=147-97$

$=50$

Hence, the required value is 50.