SOMEONE PLEASE HELP I AM BEGGING!!! Find an equation for the nth term of the arithmetic sequence. -1, 2, 5, 8, ... WITH AN EXPLANATION PLEASE I DONT UNDERSTAND
We would refer to -1, 2, 5, 8 as terms and from right to left, the first number to the left is first term and the number right after would be second term. For example, 5 would be the first term and 8 would be the second. STEP 1: Common difference To find the arithmetic sequence you must find the common difference. We are looking for the common difference in the number. This is the number that is the difference between the two terms. In order to get this, You must subtract the first from the second term. Ex: 8 equals the second term and 5 would be the first. 8-5=3 so the difference would be 3. However, to make sure the common difference is the same for the rest, it is best to check for the remaining terms. 8-5=3 5-2=3 2- -1=3 STEP 2 FINDING THE EQUATION Since the common sequence is 3, we can now find the equation. Since we subtracted in order to get the common difference, it only makes sense that we must add in order to get the next term. Add a1+d=n a1=first term n= term we are looking for (or the nth term as mentioned in your equation) d=common difference. STEP 3: Solve Plug in the number, from left to right, in the sequence into the given equation however. N is the term that must be the answer in order to have the right equation. a1+3=n a1=-1 and d=3 -1+3=2 STEP 4: Check Continue to check your answer. a1+d=n -1+3=2 2+3=5 5+3=8 and according to the equation the next sequence will be 11. So, the equation will be a1+d=n.