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Question
Find the middle term of the AP. 95, 86, 77, ........, – 247.
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Solution
Given A.P. is 95, 86, 77, ....., – 247
Here, a = 95, d = 86 – 95 = – 9
Let the A.P. has n terms.
Then, an = a + (n – 1)d
⇒ – 247 = 95 + (n – 1) (– 9)
⇒ – 247 = 95 – 9n + 9
⇒ – 247 = 104 – 9n
⇒ 9n = 104 + 247
⇒ 9n = 351
⇒ n = 39
Thus, the given A.P. has 39 terms.
Now, Middle term = `[1/2 (39 + 1)]^(th)` term
= `[1/2 (40)]^(th)` term
= 20th term
a20 = a + 19d
= 95 + 19 (– 9)
= 95 – 171
= – 76
As a result, the specified A.P.'s middle term is – 76.
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