Question:
Choose the correct answer in each of the following questions:
If $a_{n}$ denotes the $n$th term of the AP $3,8,13,18, \ldots$ then what is the value of $\left(a_{30}-a_{20}\right) ?$
(a) 40
(b) 36
(c) 50
(d) 56
Solution:
The given AP is 3, 8, 13, 18, ... .
Here, a = 3 and d = 8 − 3 = 5
$\therefore a_{30}-a_{20}$
$=[3+(30-1) \times 5]-[3+(20-1) \times 5] \quad\left[a_{n}=a+(n-1) d\right]$
$=148-98$
$=50$
Thus, the required value is 50.
Hence, the correct answer is option C.