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IMO D

arithmetic Progression => 2nd term - 1st Term = 3rd - 2nd term => x=3
therefore, given series => 4,9,14....
Hence, Nth term = a+d(n-1) = 499
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The first three terms of an arithmetic progression are 3x - 5, 2x + 3, and 5x - 1, respectively. What is the 100th term of this sequence?

3x - 5, 2x + 3, and 5x - 1 are in AP.
So, 2(2x+3) = 3x-5 + 5x-1
4x+6 = 8x-6
4x = 12
x = 3

So, a1 = 3x - 5 = 4
d = 2x+3 - 3x+5
= -x + 8
= 5

a100 = a + 99d
= 4 + 99*5
= 499

Option D

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