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Two arithmetic sequences A and B both begin with 30. Sequence A has common difference 9 and sequence B has common difference 4. What is the difference between the 51st term of A and the 51st term of B?

Answer :

LAMMETTHASHGO

The n-th term of an arithmetic sequence with first term a and common difference d is

a + (n - 1) d

So, the 51st term of A is

30 + 9 (51 - 1) = 480

while the 51st term of B is

30 + 4 (51 - 1) = 230

The difference between them 480 - 230 = 250.

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