A open chain consists of 33 diamonds with the diamond in the middle being the largest and the best?

Starting from the left end, each successive diamond till the largest diamond costs 75 euros more than the previous one and starting from the right end, each successive diamond till the largest diamond costs 175 euros more than the previous one. Find the value of the largest diamond (in euros) if the total value of diamonds on the chain is 1,64,000 euros.|||There are two arithmetical sequences, "left" and "right", which share one diamond (the one in the middle).


For "left", assume the cheapest diamond costs L euro. This means that the total value of "left" is:


L*17 + 75*16*17/2 = 17L + 10200.


For "right", we assume the cheapest diamond costs R euro. The value of "right" is:


17*R + 175*16*17/2 = 17*R + 23800.


The middle one would cost L + 75*16 and R + 175*16, which must be equal. This means:


L + 1200 = R + 2800, or L = R + 1600.


If we want to have the full value of the chain, we add the values of "left" and "right" and subtract the value of the middle diamond (which belongs to both "L" and "R" and has been counted twice):


17L + 10200 + 17R + 23800 - (R + 2800) = 164000 (this was given).


Substituting R+1600 for L gives:


17R + 27200 + 10200 + 17R + 23800 - R - 2800 = 164000


33R + 58400 = 164000


33R = 105600


R = 3200


This means the middle diamond is worth 6000 euro.