Question Video: Finding the Value of a Term in a Sequence given the General Term of That Sequence

Find the eighth term of the sequence whose 𝑛th term is given by π‘Ž_𝑛 = (6/3𝑛) βˆ’ 2, where 𝑛 ∈ ℀⁺.


Video Transcript

Find the eighth term of the sequence whose 𝑛th term is given by π‘Ž sub 𝑛 is equal to six over three 𝑛 minus two, where 𝑛 is a positive integer.

The notation 𝑧 in this case means that 𝑛 can only be an integer or whole number. As it also has the positive or plus symbol, we’re only interested in positive whole numbers. As we are asked to find the eighth term of the sequence, we’re looking to find π‘Ž sub eight. We do this by substituting 𝑛 equals eight into our 𝑛th-term formula. π‘Ž sub eight is therefore equal to six over three multiplied by eight minus two.

As three multiplied by eight is 24, we have six over 24 minus two. The fraction six over 24 can be simplified by dividing the numerator and denominator by six. This is equivalent to one-quarter. In order to subtract two from one-quarter, we could convert the two into eight-quarters. Two whole ones is equal to eight-quarters.

As our denominators are now the same, we can subtract the numerators. One minus eight is equal to negative seven. This means that the eighth term of the sequence is equal to negative seven-quarters. As seven divided by four is equal to one remainder three, this could also be written as negative one and three-quarters or as a decimal negative 1.75.

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