Find the eighth term of the
sequence whose 𝑛th term is given by 𝑎 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 𝑎 sub eight. We do this by substituting 𝑛
equals eight into our 𝑛th-term formula. 𝑎 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
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.