Question

The middle term of the AP 5, 7, 9, 11, …,165 is

• A. 75
• B. 85
• C. 95
• D. 105

Answer 1

The correct option is B 85

Given, AP: 5, 7, 9, 11,…,165
Here, first term (a) = 5, common difference (d) = 7 – 5 = 2 and last term (l) = 165
Now, l = a + (n – 1)d
$\therefore 165=5+(n-1)\times 2$
$\Rightarrow 165-5=2(n-1)$
$\Rightarrow 160=2(n-1)$
$\Rightarrow 80+1=n$
$\Rightarrow 81=n$
Thus, the total number of terms is 81.
Now, the middle term of the AP will be $\frac{81+1}{2}=\frac{82}{2}={41}^{st}$ term.
Thus, $a_{41}=a+(41-1)d$
$=5+(40\times 2)$
$=5+80$
$=85$
Hence, the correct answer is option (2).