Question

The 10th term of an Ap is -27 and the 5th term is -12
What is the 18th term

Answer 1

To find the 18th term of the arithmetic progression (AP), we need to find the common difference (d) first.

Let's find the common difference between the 10th term and the 5th term.
d = 10th term - 5th term
d = -27 - (-12)
d = -27 + 12
d = -15

Now, we can use the formula for the n-th term of an arithmetic progression:

nth term = a + (n-1)d,

where "a" is the first term and "n" is the position of the term we want to find.

We are given that the 5th term is -12, so the first term can be found using the formula:

-12 = a + (5-1)(-15)
-12 = a + 4(-15)
-12 = a - 60
a = -12 + 60
a = 48

Finally, we can use the formula to find the 18th term:

18th term = a + (18-1)d
18th term = 48 + (17)(-15)
18th term = 48 - 255
18th term = -207

Therefore, the 18th term of the arithmetic progression is -207.