The 10th term of an Ap is -27 and the 5th term is -12
What is the 18th term
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.
To find the 18th term of an arithmetic progression (AP), we need to know the common difference first. The common difference is the difference between consecutive terms in the sequence.
We are given that the 5th term of the AP is -12. Let's call it a5.
We also know that the 10th term of the AP is -27. Let's call it a10.
We can use these two terms to find the common difference (d) using the formula:
d = (a10 - a5) / (10 - 5)
Substituting the values, we have:
d = (-27 - (-12)) / (10 - 5)
d = (-27 + 12) / 5
d = -15 / 5
d = -3
Now that we have the common difference (-3), we can find the 18th term (a18) of the AP using the formula:
an = a1 + (n - 1) * d
where a1 is the first term of the AP.
To find the first term (a1), we can use the formula:
a1 = a5 - (5 - 1) * d
Substituting the values, we have:
a1 = -12 - (5 - 1) * (-3)
a1 = -12 - 4 * (-3)
a1 = -12 - (-12)
a1 = 0
Now we can find the 18th term (a18) using the formula:
a18 = 0 + (18 - 1) * (-3)
a18 = 0 + 17 * (-3)
a18 = 0 - 51
a18 = -51
Therefore, the 18th term of the given arithmetic progression is -51.
To find the 18th term of an arithmetic progression (AP), we need to determine the common difference (d) first.
Given:
10th term (a10) = -27
5th term (a5) = -12
The formula to find the nth term (an) of an AP is: an = a1 + (n - 1)d, where a1 is the first term.
To find the common difference:
a10 = a1 + (10 - 1)d
-27 = a1 + 9d ........(1)
a5 = a1 + (5 - 1)d
-12 = a1 + 4d ........(2)
Solving equations (1) and (2), we get:
-27 = a1 + 9d
-12 = a1 + 4d
Subtracting equation (2) from equation (1) to eliminate a1, we get:
-27 - (-12) = (a1 + 9d) - (a1 + 4d)
-15 = 5d
d = -15 / 5
d = -3
Now, we have the common difference (d) = -3.
To find the 18th term (a18), we can use the formula:
a18 = a1 + (18 - 1)d
Substituting the values, we get:
a18 = a1 + 17d
Since we don't have the value of a1, we cannot find the exact 18th term. However, we can find the general formula for the nth term using the given common difference.
The general formula for the nth term of an AP is:
an = a1 + (n - 1)d
So, the general formula for the nth term of this AP with a common difference (d) of -3 is:
an = a1 + (n - 1)(-3)
Please note that without knowing the value of a1, we cannot determine the exact 18th term.