They tell you that an Arith. Sequence is when each term after the 1st must be equal to the sum of the preceding # plus a constant.

They tell you P R Q T U are a set of # that meet the requirement of an Arith Sequence.

Plug in Numbers that meet that requirement for P, R, S, T, U
I chose 1 ,2, 3, 4, 5, b/c they are easy to work with and it gives us 1 as the constant

P=1 R=2 S=3 T=4 U=5 is an arith. sequence b/c if you add 1 to the preceding number it gives you the following number in the sequence
(1 + P = R, 1 +R= S)

Next step would be to plug in the #'s to the 3 choices they give you and see if they also meet the arith. sequence requirement

I) gives you 2, 4, 6, 8, 10 = sum of preceeding +2 as a constant
II) gives you -2, -1, 0, 1, 2 = sum of preceeding + 1 as a constant
III) gives your 1, 4, 9, 16, 25= sum of preceeding and constant dont form any type of pattern...

I, and II only

You can just plugin numbers and try...

the sequence could be, 1, 3, 5, 7, ...


so I would be
2, 6, 10, 14, ....

Just the differene between the numbers is doubled, but it still an arithmetic sequence..

II would be
-2, 0, 2, 4,....

again an arithmetic sequence...

III would be
1, 9, 25, 49,...
Here the difference between the numbers is not constant and hence this is not an arithmetic sequence.


Hence, only I and II are.

Hence D

An other way to look at the problem is below :

It is given that p, r, s, t u are an arithmetic sequence.

So, think 'k' is the constant

the sequence would be :

p, p+k, p+k+k, p+k+k+k, p+k+k+k+k

p, p+k, p+2k, p+3k, p+4k

I) Multiplying by 2 would make essentially the same sequence - so, TRUE
2p, 2p+2k, 2p+4k, 2p+6k, 2p+8k

II) Subtracting 3 would also make essentially same sequence - so, TRUE
p-3, p+k-3, p+2k-3, p+3k-3, p+4k-3

III) Squaring the numbers, however, would be different.
p^2, (p+k)^2 might be way off because of the squaring. so, FALSE

The point to take is that adding or multiplying any sequence with a constant basically keeps the sequence similar but squaring the elements with a constant will produce a different sequence.

Hope this helps.