Question

The first term in the sequence 5, 7, −7, ... is 5. Each even-numbered term is 2 more than the previous term and each odd-numbered term, after the first, is (−1) times the previous term. For example, the second term is 5+2 and the third term is (−1)×7. What is the 255th term of the sequence?

Answer 1

Explanation:

According to the condition, your terms are arranged as

5, 7 , -7 ,-5, 5, 7, -7, 5, -5,...................

So one loop will have 4 terms: 5, 7, -7. -5

`255 / 4 = 63 R 3`

Hence after 63 loops, the new loop has only 3 terms. That means the last loop will be 5, 7 ,-7. In other words, the 255th term will be -7