The 10th term of an AP is -27 and the 5th term is -12, what is the 18th term? Also find the sum of its 25 terms.

10th term: -27

5th term: - 12

d= -27+12/5

= -3

a+(n-1)d=-12

a+(5–1)d=-12

a+4d= -12

a=-12–4d

a=-12-(4×-3)

a=-12+12=0

18  term=a + (18–1)d

=0+(17×-3)

51

a+9d=-27(1)

a+4d=-12(2)

make a the subject of equation 2 and put into equation 1

-12+4d+9d=-27

-12+13d=-27

d=-15\13

put d into equation 1

a+9(-15/13)=-27

a=16.6

a+17d=x

17+16.6(-15/13)

x=-2 is the 18th term

25÷2(16.6+15.6(-15/13)

=-208.4

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)