Class 10

Math

All topics

Arithmetic Progressions

Find the first term $a_{1}$ and the common difference $d$ of the arithmetic progression in which $a_{2}+a_{5}−a_{3}=10$, $a_{2}+a_{9}=17$

$a_{t}=a_{1}+(t−1)da_{2}+a_{5}−a_{3}=10,a_{2}+a_{9}=17(a_{1}+d)+(a_{1}+4d)−(a_{1}+2d)=10a_{1}+3d=10−(i)a_{1}+d+a_{1}+8d=172a_{1}+9d=17−(ii)×1a_{1}+3d=10−(i)×23d=−3d=−1$

Putting value in $(ii)$

$a_{1}−3=10a_{1}=13$

Answer, $a_{1}=13$ & $d=−1$