Question Video: Finding the Value of a Term in an Arithmetic Sequence given the General Term of This Sequence Mathematics • Second Year of Secondary School

Video Transcript

Find 𝑎 50, given the arithmetic sequence 𝑎 𝑛 equals seven 𝑛 minus one.

The notation 𝑎 50 means the 50th term in the sequence, where 𝑎 one is the first term, 𝑎 two the second term, and so on. In order to calculate the 50th term, we substitute 50 into the expression seven 𝑛 minus one. This gives us the calculation seven multiplied by 50 minus one.

Seven multiplied by five is equal to 35. Therefore, seven multiplied by 50 is 350. Subtracting one from this gives us 349. The 50th term, 𝑎 50, in the arithmetic sequence 𝑎 𝑛 equals seven 𝑛 minus one is 349. We can use this method to work out any term in the sequence.