Question

Let $a_1, a_2, \ldots, a_n$ be in AP If $a_5=2 a_7$ and $a_{11}=18$, then $12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots+\frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$ is equal to

Answer 1

The correct answer is 8.
2a5​=a5​( given )
2(a1​+6d)=a1​+4d
a1​+8d=0....(1)
a1​+10d=18...(2)
By (1) and (2) we get a1​=−72,d=9
a18​=a1​+17d=−72+153=81
a10​=a1​+9d=9
12(da11​​−a10​​​+da12​​−a11​​​+……da18​​−a17​​​)
12(da18​​−a10​​​)=912(9−3)​=612×6​=8