This week we learned about arithmetic sequences which is where each number in a pattern increases or decreases by the same number every time. One of the concepts I found interesting was when given the term number in an arithmetic sequence, you could find out the exact number that term is associated with. To elaborate, if the question gives an arithmetic sequence of 2, 4, 6… and asks you to find term 13, you can do so using the formula t3+nd=t13.
Firstly, to solve it you’d take the formula and you’d replace t3 with 6 because term three is equal to 6. Then you’d replace n with 10 because there are 10 terms in between t3 and t13. After that replace d with 2, because the pattern increases by 2 which is also know as the common difference. The formula should now look like this: 6+10(2)=t13.
After you have this equation, you can begin to solve it using algebra. Multiply 10 and 2 so that the formula becomes 6+20=t13. Next, add 20 and 6 together so that you get 26=t13. Now you know that the thirteenth term in the sequence is equal to 26.