SOLUTION: The 10th term of A.P is -5 and the 34th term is -57. Find the 15th term

Question 981409: The 10th term of A.P is -5 and the 34th term is -57. Find the 15th term

Answer by Timnewman(323) (Show Source): You can put this solution on YOUR website!
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.
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