Question

Choose the correct answer in each of the following questions:

If a_n denotes the nth term of the AP 3, 8, 13, 18, ... then what is the value of $\left(a_{30}-a_{20}\right)$?

(a) 40 (b) 36 (c) 50 (d) 56

Answer 1

The given AP is 3, 8, 13, 18, ... .

Here, a = 3 and d = 8 − 3 = 5

$$\begin{gathered} \therefore a_{30}-a_{20} \\ =\left[3+\left(30-1\right)\times 5\right]-\left[3+\left(20-1\right)\times 5\right]\left[a_n=a+\left(n-1\right)d\right] \\ =148-98 \\ =50 \end{gathered}$$

Thus, the required value is 50.

Hence, the correct answer is option C.