Class 11

Math

Algebra

Sequences and series

$x_{1},x_{2},x_{3}$, ________ are in A.P. If $x_{1}+x_{7}+x_{10}=−6$ and $x_{3}+x_{8}+x_{12}=−11$, then $x_{3}+x_{8}+x_{22}=$ __________.

- $−21$
- $−15$
- $−18$
- $−31$

$x_{1}+x_{7}+x_{10}=−6$

$⇒(a)+(a+6d)+(a+9d)=−6$

$⇒3a+15d=−6→eqn(1)$

$x_{3}+x_{8}+x_{12}=−11$

$⇒(a+2d)+(a+7d)+(a+11d)=−11$

$⇒3a+20d=−11→eqn(2)$

Solving eqn (1) and (2), we get $a=3$ and $d=−1$

Now, $x_{3}+x_{8}+x_{22}=3a+30d=−21$

So, option (A)