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The middle term of the AP 11, 8, 5, …,-79 will be?(a) 30(b) -34(c) 34(d) -30This question was addressed to me in my homework.I would like to ask this question from Arithmetic Progression Basics in division Arithmetic Progressions of Mathematics – Class 10

Answer»

The correct choice is (b) -34

The explanation is: Here a = 11 and d = 8 – 11 =-3

Let the given AP contain N terms.

Tn = -79

a + (n – 1)d = -79

11 + (n – 1) – 3 = -79

11 – 3n + 3 =-79

14 + 79 = 3n

n = 31

Thus, the given AP has 31 terms.

∴ its middle term =\(\FRAC {1}{2}\) (31 + 1) = 16^th term

∴ 16^thterm = 11 + (16 – 1) – 3 = 11 – 45 =-34



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