The first term of a sequence is 𝑎
zero which is equal to 20. The 𝑡 plus oneth term of the
sequence is given by 𝑎 of 𝑡 plus one is equal to three multiplied by 𝑎 of 𝑡. Find 𝑎 of four.
As 𝑎 of zero is equal to 20, we
can use the formula 𝑎 of 𝑡 plus one is equal to three multiplied by 𝑎 of 𝑡 to
work out 𝑎 one, then 𝑎 two, 𝑎 three, and finally 𝑎 four. In order to calculate 𝑎 one, we
need to multiply 𝑎 zero by three. Three multiplied by 20 is equal to
60. Therefore, 𝑎 one is equal to
60. 𝑎 two can be calculated in the
same way by multiplying 𝑎 one by three. Three multiplied by 60 is 180. Therefore, 𝑎 two is equal to
We can repeat this method to
calculate 𝑎 three. Three multiplied by 180 is equal to
540. Finally, 𝑎 four can be calculated
by multiplying 𝑎 three by three. Three multiplied by 540 is
Using the iterative method of
multiplying the previous term by three gives us a value of 𝑎 four of 1620.