Question

Find a formula for the general term of the sequence, assuming that the pattern of the first few terms continues.

Answer 1

Step 1:

The sequence .

The first term of sequence .

The second term of sequence .

The third term of sequence .

Observe the sequence the numerator is starts with 1 and next numerators are 4, 9, 16.

Those are squares of natural numbers .

The denominator is starts with 2 and next denominators are 3, 4, 5...

The denominator sequence is increases with 1 unit, the term denominator is .

The even terms are negative, so the sequence is multiplied with .

The general term of the sequence is .

Solution:

The general term of the sequence is .