The 3rd term of an arithmetic progression is -5 if if the 5th term is 4.5 find the 11th term
To solve this problem, we need to find the common difference (d) of the arithmetic progression first.
The 3rd term is given as -5, so we can write the equation:
a + 2d = -5 ........(1) (where a is the first term)
The 5th term is given as 4.5, so we can write the equation:
a + 4d = 4.5 ........(2)
Now, we have two equations:
a + 2d = -5 ........(1)
a + 4d = 4.5 ........(2)
To solve these equations, we can subtract equation (1) from equation (2):
(a + 4d) - (a + 2d) = 4.5 - (-5)
2d = 9.5
d = 9.5/2
d = 4.75
Now that we have found the common difference (d), we can find the first term (a) by substituting d into equation (1):
a + 2(4.75) = -5
a + 9.5 = -5
a = -5 - 9.5
a = -14.5
So, the first term (a) is -14.5 and the common difference (d) is 4.75.
Now, we can find the 11th term (T11) by using the formula for arithmetic progression:
Tn = a + (n-1)d
T11 = -14.5 + (11-1) * 4.75
T11 = -14.5 + 10 * 4.75
T11 = -14.5 + 47.5
T11 = 33
Therefore, the 11th term of the arithmetic progression is 33.