Question

The 10th term of an ap is -27and the 5th term is -12what is the 18th term

Answer 1

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

Answer 2

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