### Video Transcript

Express the series 54 multiplied by
12 plus 54 multiplied by 24 plus 54 multiplied by 36, and so on, all the way up to
54 multiplied by 240 in sigma notation.

In this question, we are given the
first three terms of our series. Together with the πth or final
term. We have been asked to express this
series using sigma notation as shown. We need to find an expression for
the general term π’ sub π and the number of terms in the series π. We notice that each of our terms is
the product of two numbers. The first number is 54 in each of
our terms. The second number corresponds to
the multiples of 12. We have 12 times one, 12 times two,
12 times three, and so on. The final term is equal to 12
multiplied by 20. This means that the general term
for our series is 54 multiplied by 12π where π is a variable going from one to
20.

54 multiplied by 12 is equal to
648. Therefore, 54 multiplied by 12π is
648π. Using sigma notation, we can
therefore express the series as the sum of 648π where π takes values from one to
20.