NMTC 2015

Algebra Level 3

An arithmetical progression has positive terms.The ratio of the difference of the 4th and 8th term to the 15th term is 4 15 \frac { 4 }{ 15 } and the square of the difference of the 4th and the 1st term is 225.Which term of the series is 2015?

403 225 404 410

Bala Vidyadharan by Bala vidyadharan , 20, India

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3 solutions

Raj Rajput
Aug 24, 2015

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Arjen Vreugdenhil
Sep 18, 2015

Let the progression be given as a n = a 0 + n d a_n=a_0+nd , then 4 d a 0 + 15 d = 4 a 0 / 4 + 15 = 4 15 , \frac{4d}{a_0+15d}=\frac{4}{a_0/4+15}=\frac{4}{15}, so that a 0 = 0 a_0 = 0 and a n = n d a_n = nd .

The second statement shows that ( 4 d − d ) 2 = 9 d 2 = 225 , (4d-d)^2=9d^2=225, so that d = 5 d = 5 .

Finally, n = 2015 5 = 403. n=\frac{2015}{5}=403.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ayush G Rai
Jun 17, 2016

I had already posted this question. https://brilliant.org/profile/ayush-95mh3z/sets/algebra/416345/problem/arithmetic-progressions-3-2/

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