The 10th term of an ap is -27and the 5th term is -12what is the 18th term
In an Arithmetic Progression:
an = a1 + ( n - 1 ) d
where
a1 = the initial term
an = the nth term
a10 = a1 + 9 d = - 27
a5 = a1 + 4 d = - 12
Now solve system of two equations:
a1 + 9 d = - 27
a1 + 4 d = - 12
The solution is:
a1 = 0 , d = - 3
a18 = a1 + 17 d = 0 + 17 ∙ ( - 3 ) = 0 - 51 = - 51
nth term=a+(n-1)d
-27=a+(10-1)d
-27=a+9d
a+9d=-27....eqn (i)
-12=a+(5-1)d
-12=a+4d
a+4d=-12....eqn (ii)
a+9d=-27
a+4d=-12
solve by elimination method
5d=-15
d=-3
a+(4×-3)=-12
a-12=-12
a=-12+12
a=0
18th term= 0+(18-1)×-3
=17×-3
=-51