Question

if sum of 3rd and 8th terms of an A.P. is 7 and sum of 7th and 14th term is -3 then find the 10th term

Answer 1

[a+2d]+[a+7d]=7
a+2d+a+7d=7
2a+9d=7                                       1

[a+6d]+[a+13d]=-3
a+6d+a+13d=-3
2a+19d=-3                                     2


multiply the eqn 1*19 and eqn 2*9 then subtract
38a+171d=133
18a+171d=-27
-     -           +
----------------------
20a=160
a  =    160/20
a  =   8
put the value of a in  eqn 1
2a+9d=7
2*8+9d=7
16+9d=7
9d=7-16
9d  =   -9
d  =  -9/9
d  =  -1
a/c to question,
10th terms=   [a+9d]
                 =   [8+9*-1]
                 =   8-9
                 =   -1