find the middle term of AP 10,7,4,.....,-62
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Answer,
First term of the AP = 10
Common difference = d = 7 - 10 = - 3
Last term = - 62
Since,
an = a + (n - 1) × d
∴ - 62 = 10 + (n - 1) × (-3)
⇒ - 62 - 10 = - 3n + 3
⇒ - 72 = - 3n + 3
⇒ - 72 - 3 = - 3n
⇒ 3n = 75
⇒ n = 75/3 = 25
∴ Middle term is (25 + 1)/2 = 13th
So, a13 = a + (13 - 1) × d
∴ a13 = 10 + 12 × (-3)
⇒ a13 = 10 - 36 = - 26
∴ Middle term of the AP is - 26.
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