Question

In an $A.P$ the ${15}^{th}$ term is $74$ and ${26}^{th}$ term is $118$. Find the first term and the common difference and also the ${45}^{th}$ term.

Answer 1

$74=a+14d$

$118=a+25d$

$44=11d$

$d=4$

$74=a+56$

$a=18$

$S_n=[a+(n-1\left)d\right]\frac{m}{2}$

$=\frac{45}{2}[18+44(4\left)\right]=\frac{45}{2}[18+116]$

$=\frac{45}{2}\left[194\right]=45\times 97=4365$

$a_{45}=18+\left(44\right)4=194$