Question

Find the sum of the first 12 terms of the sequence. Show all work for full credit. 1, -4, -9, -14, . .

Answer 1

Hello there!

First, let's figure out our rule for the first 4 given terms.
1, -4, -9, -14.

The rule appears to be (n - 5);
1 - 5 = -4
-4 - 5 = -9
-9 - 5 = -14
Let's continue to apply this rule 8 more times.
1.) -14 - 5 = -19
2.) -19 - 5 = -24
3.) -24 - 5 = -29
4.) -29 - 5 = -34
5.) -34 - 5 = -39
6.) -39 - 5 = -44
7.) -44 - 5 = -49
8.) -49 - 5 = -54

Now we have our complete sequence. All we have to do now is sum the numbers up.
Remember, when adding a negative to a negative, you're doing the same thing as adding two positive numbers.

1 - 4 = -3
-3 - 9 = -12
-12 - 14 = -26
-26 - 19 = -44
-44 - 24 = -68
-68 - 29 = -97
-97 - 34 = -131
-131 - 39 = -170
-170 - 44 = -214
-214 - 49 = -263

The sum of your sequence is -263.

I hope this helps!
-Ekansh NImbalkar