Arithmetic Progression

Level 2

If the first four terms of an arithmetic progression are a,2a,b and a-6-b for some numbers a and b,then the value of the 100 th term is :-


The answer is -100.

Mayank Devnani by Mayank Devnani , 22, India

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1 solution

Karthik Sridhar
Feb 25, 2015

d = t 2 − t 1 = 2 a − a = a d=t_2-t_1=2a-a=a

d = a = b − 2 a d=a=b-2a

∴ 3 a = b \therefore 3a=b ...................(1)

b − 2 a = a − 6 − 2 b b-2a=a-6-2b

∴ 3 b − 3 a = − 6 \therefore 3b-3a=-6

∴ b − a = − 2 \therefore b-a=-2 ..................(2)

By solving these equations simultaneously, we get a = − 1 a=-1 and b = − 3 b=-3 .

Now, solving the AP, a = − 1 , d = − 1 a n d n = 100 a=-1,~d=-1~and~n=100 .

∴ a n = − 1 − 99 \therefore a_n=-1-99

∴ a n = − 100 \therefore\boxed{a_n=-100}

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