Question 981409
Hi,
Recall that the nth term of an A.P is giving by;T(n)=a+(n-1)d
where a=first term
 d=commom difference.
Now, if 10th term is -5,
Therfore, a+9d=-5----(1)
 also,if  34th term is -57,
then, a+33d=-57-----(2) 
from equ (1),
 a=-5-9d----(3)
substitute for a in equ (2)
i.e, -5-9d+33d=-57
 24d=-57+5
24d=-52
dividing bothsides by 24,
d=-13/6
put d in equ (1) 
 a=-5-9d
a=-5-9(-13/6)
a=-5+39/2
a=29/2
15th term(T(15)) =a+14d 
 but a=29/2
 d=-13/6
15th term=(29/2)+14(-13/6)
  =-95/6
You can put in mixed frction.