Question

The sum of the first five terms of 3,-9,27,-81

Answer 1

183

Explanation:

The answer above is correct, but I do want to elaborate on how to receive this answer;

This pattern takes an alternate of positive and negative numbers at a time. If you can see for each positive number, there is a negative consecutively. Imagine these values were all positive. What would then be the difference between each? 3 * 3 = 9, 9 * 3 = 27, 27 * 3 = 81, and so each number would be 3 times the other. Now let us go back to the state we have at hand, negative and positive numbers. 81 * 3 = 243, and as we alternate between negative and positive numbers, 243 should be positive as the previous number - 81, is negative. We have now received our 5th term!

The questions asks us to determine the sum of each of the terms however, so let us do so;

`3 - 9 + 27 - 81 + 243,\\- 6 + 27 - 81 + 243,\\21 - 81 + 243,\\- 60 + 243,\\\\183\\Solution = 183`

Hope that helps as well!