3,5,-5...

The first term in the sequence of #'s shown above is 3. Each even # term is 2 more than the previous term and each odd # term, after the first, is -1 times the previous term. For example, the second term is 3+2, and the third term is (-1)x5. What is the 55th term of the sequence?

a.-5
b.-3
c.-1
d.3
e.5

The Answer is: (A)-5 H0w did they arrive at that answer???

lets look at the sequence. Check me.

3,5,-5,-3,3,5,-5, -3, 3, 5, -5, ..

Notice the terms 3, 7, 11 are all -5. So one can predict that the thirteenth term, 17, 21 term and so on will be -5.

Each fourth term after the third is -5.

the 20 +3 term is 5 spaces of 4's after 3, the 40 + 3 term is 10 spaces of 4, the 52+3 term is 13 spaces of 4, so that means the 55 term is -5

Therefore, the answer is (A)-5

To arrive at the answer of -5 for the 55th term of the sequence, we can observe the pattern in the sequence:

The first term is 3.
Each even-numbered term is 2 more than the previous term.
Each odd-numbered term, after the first, is -1 times the previous term.

So, let's break down the terms step by step:

1st term: 3
2nd term: 3 + 2 = 5
3rd term: -1 * 5 = -5
4th term: -5 + 2 = -3
5th term: -1 * -3 = 3
6th term: 3 + 2 = 5
7th term: -1 * 5 = -5
8th term: -5 + 2 = -3

We can see that the pattern repeats after every 4 terms: -5, -3, 3, 5. And as you correctly noticed, the 13th term, 17th term, 21st term, and so on, is -5.

Since 55 is three terms beyond the last occurrence of -5, we can determine that the 55th term is also -5.

Therefore, the answer is (a) -5.

To arrive at the answer of -5 for the 55th term of the sequence, you need to understand the pattern in the sequence.

The first term is 3. Then, for each even-numbered term, you add 2 to the previous term. So the second term is 3 + 2 = 5.

For each odd-numbered term (starting from the third term), you multiply the previous term by -1. So the third term is -1 * 5 = -5.

The cycle repeats with the fourth term being the previous term + 2 (so -5 + 2 = -3), and the fifth term being the negative of the previous term (so -1 * -3 = 3).

This pattern continues: 3, 5, -5, -3, 3, 5, -5, -3, 3, 5, -5...

To find the 55th term, you can observe that every 12 terms, the sequence repeats. So the 13th term, 17th term, 21st term, etc. will all be -5.

To determine the position of the 55th term within this repeating pattern, you can subtract 3 from 55 (because the first term is 3). This gives you 52. Divide 52 by 4 (since there are 4 terms in each repetition) and you get 13, with a remainder of 0.

Since the remainder is 0, you know that the 55th term is in one of the positions in the sequence where the term is -5. And from the observation earlier that the 13th term is -5, you can conclude that the 55th term is also -5.

Therefore, the answer is (A) -5.