Question

Choose the correct answer in each of the following questions:

The 7th term of an AP is −1 and its 16th term is 17. The nth term of the AP is [CBSE 2014]

(a) (3n + 8) (b) (4n − 7) (c) (15 − 2n) (d) (2n − 15)

Answer 1

Let a be the first term and d be the common difference of the AP. Then,

nth term of the AP, a_n = a + (n − 1)d

Now,

$$\begin{gathered} a_7=-1\left(\mathrm{Given}\right) \\ \Rightarrow a+6d=-1.....\left(1\right) \end{gathered}$$

Also,

$$\begin{gathered} a_{16}=17\left(\mathrm{Given}\right) \\ \Rightarrow a+15d=17.....\left(2\right) \end{gathered}$$

Subtracting (1) from (2), we get

$$\begin{gathered} \left(a+15d\right)-\left(a+6d\right)=17-\left(-1\right) \\ \Rightarrow 9d=18 \\ \Rightarrow d=2 \end{gathered}$$

Putting d = 2 in (1), we get

$$\begin{gathered} a+6\times 2=-1 \\ \Rightarrow a=-1-12=-13 \end{gathered}$$

∴ nth term of the AP, a_n = −13 + (n − 1) × 2 = 2n − 15

Hence, the correct answer is option D.