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Algebra Level 1

Aryan got $-10$ marks in his first exam and $15$ marks in his $15^{\text{th}}$ exam.

If all his marks follow an arithmetic progression with a positive common difference, in which exam did he get zero marks?

5^\text{th}

6^\text{th}

He never got zero marks None of the above

5 solutions

Nishant Singh
Aug 10, 2015

The common ratio is d= 25/14 according to which 0 shall never come.

I think you made a typo error, the common difference must be $\dfrac{5}{14}$ .

A Former Brilliant Member - 4 years, 1 month ago

15 = -10 + (15-1)d.. How did you get d to be 5/14 here?

Aondofa Samuel - 3 years, 7 months ago

I think he took +ve10 instead of -ve 10

Sriram Hs - 2 years, 1 month ago

Yes the common difference is 5/14

Hence

0 = a + (n - 1 ) d 0 = 10 + ( n - 1 ) 5/14 0 = 10 + 5n/14 - 5/14

We take fraction LCM

0 = 140 + 5n - 5

Like terms

0 = 135 + 5n

135 = -5n

Divide both side by 5

n = -27

Obinna Jonnas - 11 months ago

Zie Zzoll
Jan 9, 2018

The common difference is 25/14 so if 0 was a term in the AP then the solution to 0 = -10 + (n - 1)25/14 would be a natural number. As it is 6.6 we know that 0 is not a term in the AP.

A Former Brilliant Member
May 14, 2017

Since the first exam is $-10$ marks and the $15^{th}$ exam is $15$ marks and the common difference is positive, $zero~marks$ is not possible.

May I bring to your kind notice that the marks in the first exam is -10, not 10.

Nilabha Saha - 3 years, 11 months ago

Thanks. I updated my solution.

A Former Brilliant Member - 3 years, 11 months ago

Qian Chen
Mar 30, 2021

华文：第一个是十分，第十五个是十五分。变多了。第一个是十分的话怎么可能有零分？ ... English：Aryan got 10 marks in his first exam and 15 marks in his 15th exam. 15th exam is more than 1st exam. If the 1st exam is already 10, how is it possible that in one of the exams he only got 10 marks? ... Melayu: Yang pertama adalah sepuluh mata dan yang kelima belas adalah lima belas mata. Lebih banyak lagi. Bagaimana boleh ada titik sifar jika yang pertama adalah sepuluh?

No the common difference must be 5/14

Qian Chen - 2 months, 2 weeks ago

Debojyoti Bagchi
Mar 5, 2020

It does not require calculation. The problem statement says common difference is positive. If the sequence has started from a positive number, and C.D is positive, then no member of the sequence could be zero.

It doesn't start from a positive number. The initial value is -10

Ahmed Maged - 11 months, 3 weeks ago