Question

The 3rd term of an arithmetic progression is -5 if if the 5th term is 4.5 find the 11th term

Answer 1

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.