Question

Which term of the AP 20,77/4,37/2,71/4...is its first negative term?
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Answer 1

Hence, the first negative term would be the 28th term.

Answer 2

Step-by-step explanation:

d = 77/4 - 20 => (77- 80)/4 = -3/4

for first negative term, aₙ < 0

aₙ = a + (n - 1)d < 0

=> a = 20, d = -3/4 and n is to be found out

=> 20 + (n - 1) × -3/4 < 0

=> 20 - 3n/4 + 3/4 < 0

=> 20 + 3/4 < 3n/4

=> 83/4 < 3n/4

=> 83 < 3n [ 4 cancels out on both sides ]

=> 3n > 83

=> n > 83/3

=> n > 27.66666

=> n = 28

therefore the 28th term is the first negative term of the given sequence