The following sequence reads: 8, 5, 2, -1. What are the 4th and 50th terms of this sequence?

With sequences we should follow the general formula of An + B.

The refers to the position in the sequence i.e. for the 3rd number in the sequence (which is 2 in the above sequence) n=3.

The A refers to the difference between each number in the sequence. In the case of the sequence above, A= -3 (each number is 3 lower than the previous one in the sequence). 

The refers to the difference between a particular number in the sequence compared with the number in the same position if it were the 'expected sequence'. In other words if it were just An. So for the sequence above it would be -3n so plugging in n=1, the first value in the sequence would be -3 x 1 = -3.

However we can see that this isn't the case, the first number is actually 8. 8 is 11 higher than -3 (8 - -3 = 8+3 = 11). So B=11.

Therefore the general formula for this sequence is -3n + 11.

All we now have to do is plug in the values for the poisiton in the sequence into n.

So the 4th term in the sequence is when n = 4:

(-3 x 4) = -12 + 11 = -1

And the 50th term in the sequence is when n = 50:

(-3 x 50) = -150 + 11 = -139

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