Q. If both the sequences x, a1, a2, y and x, b1, b2, z are in A.P. and it is given that y > x and z < x, then which of the following values can
A 2
B 5
C -3
D 1
E 0
EXPLANATION
C
The two given sequences in AP are : x, a1, a2, y and x, b1, b2, z. Additionally, it is given that : y > x and z < x. Hence the common difference is not zero for both the series : Since y > x the common difference is positive for the first series. (Considering the common difference to be d1) Similarly z < x the common difference is negative for the given series. (Considering the common difference to be d2) Now for the given value :
The value of a1 – a2 is negative and b1 – b2 is positive.
Hence the value of takes a negative value
The only possible option is -3.
The answer is option C.
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