Question

The ${10}^{th}$ and ${18}^{th}$ term of an $A.P.$ are $41$ and $73$ respectively. Find the ${26}^{th}$ term of the same $A.P.$

Answer 1

$a_{10}=a+9d=41$ ...(1)

$a_{18}=a+17d=73$ ...(2)

$\left(1\right)-\left(2\right)$

$a+9d-a-17d=41-73$

$8d=32$

$d=4$

eqn (1) $\Rightarrow a+36=41$

$\Rightarrow a=5$

$a_{26}=a+25d$

$=5+25\times 4$

$=105$