The 3rd term of and a.p is 9 while the 11th term is -7.find the 5th term of and a.p
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To find the 5th term of an arithmetic progression (AP), we need more information. In this case, we are given the 3rd term and the 11th term of the AP.
Let's use the formula for the nth term of an arithmetic progression:
an = a + (n - 1)d
Where:
an = nth term of the AP
a = first term of the AP
n = position of the term
d = common difference between terms
Given that the 3rd term is 9, we have:
a3 = a + (3 - 1)d = 9
Similarly, for the 11th term being -7:
a11 = a + (11 - 1)d = -7
Now we have two equations with two unknowns (a and d).
From the equation a3 = 9, we get:
a + 2d = 9 ----(1)
From the equation a11 = -7, we get:
a + 10d = -7 ----(2)
Now, we can solve these two equations simultaneously to find the values of a and d. Let's subtract equation (1) from equation (2) to eliminate 'a':
(a + 10d) - (a + 2d) = -7 - 9
8d = -16
d = -16/8
d = -2
Substituting the value of d back into equation (1):
a + 2(-2) = 9
a - 4 = 9
a = 9 + 4
a = 13
Therefore, the first term 'a' is 13 and the common difference 'd' is -2.
Now we can find the 5th term (a5) using the formula:
a5 = a + (5 - 1)d
= 13 + 4(-2)
= 13 - 8
= 5
Hence, the 5th term of the arithmetic progression is 5.