Question

Very-Short and Short-Answer Questions

If a_n denotes the nth term of the AP 2, 7, 12, 17, ... , find the value of (a₃₀ − a₂₀). [CBSE 2011]

Answer 1

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

Here, a = 2 and d = 7 − 2 = 5

$$\begin{gathered} \therefore a_{30}-a_{20} \\ =\left[2+\left(30-1\right)\times 5\right]-\left[2+\left(20-1\right)\times 5\right]\left[a_n=a+\left(n-1\right)d\right] \\ =147-97 \\ =50 \end{gathered}$$

Hence, the required value is 50.