Discussion
In an A.P, \(t_{7} - t_{4} = 20\). Which one of the following is false?
Answer: D
Since \(t_{7}-t_{4}=3d=20\), the common difference is \(d=\tfrac{20}{3}\), which fixes d but not the first term, so (A) is true.
The difference between the 10th and 1st terms is 9d = 60, so (B) is true, and the A.M. of the 12th and 20th terms is the 16th term, so (C) is true. The A.M. of the 5th and 30th terms is the \(\tfrac{5+30}{2}=17.5\)th term, not the 17th, so (D) is false.
Since d = 20/3, the 10th term minus the first is 9 x 20/3 = 60, which agrees with statement (B).
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