Question

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 =:

Answer 1

The answer is -21

1) Let the first term of AP be a and Common difference be d

2) Given First equation x1+x7+x10 =-6

3) Substituting the values of terms a +(a+6d)+(a+9d) =-6

3a +15d=-6

4) Given second equation x3 +x8 +x12 = -11

5) Substituting the value of terms

a+2d + a+7d + a+11d = -11

3a + 20d =-11

6) Subtracting first equation from second (3a+20d)-(3a+15d) = -11+6 = -5

5d=-5

d=-1

7) putting the value in first equation

a=3

8) Value to be find is xe+x8+x22

= a+2d+a+7d+a+21d = 3a + 30d

= 9-30=-21