Question Video: Finding the General Term of a Given Arithmetic Sequence Mathematics

Find, in terms of 𝑛, the general term of the sequence (44, 70, 96, 122, ...).

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Video Transcript

Find, in terms of 𝑛, the general term of the sequence 44, 70, 96, 122, and so on.

Any arithmetic sequence has first term π‘Ž and common or first difference 𝑑. The first term in our sequence is 44. Therefore, π‘Ž is 44. In order to get from 44 to 70, we add 26. The same is true from 70 to 96 and from 96 to 122. This means that the common difference 𝑑 of this sequence is 26. The general or 𝑛th term π‘Ž sub 𝑛 of any arithmetic sequence is equal to π‘Ž plus 𝑛 minus one multiplied by 𝑑.

Substituting in our values of π‘Ž and 𝑑 gives us 44 plus 𝑛 minus one multiplied by 26. We can expand the brackets or distribute the parentheses by multiplying 26 by 𝑛 and 26 by negative one. This gives us 44 plus 26𝑛 minus 26. Collecting like terms gives us 26𝑛 plus 18. Therefore, the general term of the sequence 44, 70, 96, 122 is π‘Ž sub 𝑛 is equal to 26𝑛 plus 18.

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