In sequence P, P4 and P5 are 11 and 9 respectively. Each term after th

Notice that as per the question statement "Each term after the first two terms in sequence P is either the sum of the previous two terms if that sum is odd, or half the sum of the previous two terms if the sum is even."

We can find out the value of \(P_3 \) by infering what's happening between \(P_3\) and \(P_4\) to results in \(P_5\)

If the sum of \(P_3\) and \(P_4\) were to be odd, \(P_5\) would have been greater than \(P_4\) i.e. greater than 11.

However, since \(P_5\) is less than \(P_4\), this is only possible if we have \(P_5\) equal to half the sum of \(P_3\) and \(P_4\).

Therefore, sum of \(P_3\) and \(P_4\) must be even.

rahulp11

What you did makes intuitive sense...however, if the question had asked for the largest possible value of P2 rather than the largest possible product of P1 and P2, your method would have yielded an incorrect result...this is because there's nothing in the question that requires any of the terms (aside from P4 and P5) to be positive.

We could have -28, 24, -2, 11, 9
Or -17, 13, -2, 11, 9


BhavyaJha

What rahulp11 was doing was saying that since we added something to P4 and then ended up with a smaller number for P5, we must have had to invoke the "divide by two" clause in getting from P4 to P5. What divided by two results in 9? 18. We needed P3+P4=18 and we had P4=11, so P3=7. As you can see from above, there's another way to get to P5=9 other than making P3=7 (the other way is making P3=-2), but that other way ends up with a negative value for P1*P2, so it doesn't impact the final answer.



Does all of that make sense?