maths help

Question

There are 30 terms in an arithmetic pregression.
The 2nd and 3rd terms are distinct integers.
The ratio of the 1st 20 terms and the sum of the 1st 10 terms equals twice the ratio of the 2nd and the 1st terms.Which of the following can b the sum of all its terms?

Answer 1

This problem can be solved by writing  S₂₀ / S₁₀  =   2 a₂ / a₁  =   2( a₁  + d )/ a₁

Use the formula for the sum of the first n terms of an arithmetic series:

    S_n = n (2 a₁ +(n-1) d )/2     where a₁ is the first term and d is the common difference.

 

After some algebraic rearrangement, the following results:  d/a₁ =  8/9.    Since the first two terms are distinct integers, both a₁ and d must be integers.   So a possible conclusion is   d = 8   and  a₁ = 9.    This can be verified by direct substitution into the first equation.    The sum of all the terms is S₃₀  which works out to 3750

Answer 2

Is this a multiple choice question? If so, what are your choices?