Question

The 10th and 18th terms of an $A.P$ are 41 and 73 respectively. Find the 26 th term.

Answer 1

Let the first term be $a$ and common difference be $d$ then

$a_{10}=41\Rightarrow a+9d$

$a_{10}=73\Rightarrow a+17d$

$\Rightarrow a+9d+8d=73$

$\Rightarrow 41+8d=73$

$\Rightarrow 8d=73-41$

$\Rightarrow 8d=32\Rightarrow d=4.$

$\therefore a+9d=41$

$\Rightarrow a+9\times 4=41$

$\Rightarrow a=5$

Hence,

The ${26}^{th}$ term $=a+25d\Rightarrow 5+25\times 4\Rightarrow 105.$

This is the required answer.