# Choose the correct answer in each of the following questions:

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

(a) $(3 n+8)$

(b) $(4 n-7)$

(c) $(15-2 n)$

(d) $(2 n-15)$

Solution:

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

nth term of the AP, aa + (− 1)d

Now,

$a_{7}=-1$                                (Given)

$\Rightarrow a+6 d=-1 \quad \ldots(1)$

Also,

$a_{16}=17$                             (Given)

$\Rightarrow a+15 d=17 \quad \ldots(2)$

Subtracting (1) from (2), we get

$(a+15 d)-(a+6 d)=17-(-1)$

$\Rightarrow 9 d=18$

$\Rightarrow d=2$

Putting d = 2 in (1), we get

$a+6 \times 2=-1$

$\Rightarrow a=-1-12=-13$

$\therefore n$th term of the AP, $a_{n}=-13+(n-1) \times 2=2 n-15$

Hence, the correct answer is option D.