1
Question
x1,x2,x3,... are in A.P. If x1+x7+x10=−6 and x3+x8+x12=−11, then the value of x3+x8+x22 is
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Solution
The correct option is D −21
Let the common difference =d.
x1+x7+x10=−6
x1+x1+6d+x1+9d=−6 ..........(i)
and x1+2d+x1+7d+x1+11d=−11 ..........(ii)
(i) becomes 3x1+15d=−6
(ii) becomes 3x1+20d=−11
(i) - (ii) gives −5d=5⇒d=−1
From (i), 3x1+15(−1)=−6⇒x1=3
Now, x3+x8+x22=x1+2d+x1+7d+x1+21d
=3x1+30d
=3(3)+30(−1)
=−21
Let the common difference =d.
x1+x7+x10=−6
x1+x1+6d+x1+9d=−6 ..........(i)
and x1+2d+x1+7d+x1+11d=−11 ..........(ii)
(i) becomes 3x1+15d=−6
(ii) becomes 3x1+20d=−11
(i) - (ii) gives −5d=5⇒d=−1
From (i), 3x1+15(−1)=−6⇒x1=3
Now, x3+x8+x22=x1+2d+x1+7d+x1+21d
=3x1+30d
=3(3)+30(−1)
=−21
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