Video: Pack 1 • Paper 2 • Question 15

Pack 1 • Paper 2 • Question 15

01:40

Video Transcript

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 180.

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 1620.

Using the iterative method of multiplying the previous term by three gives us a value of 𝑎 four of 1620.

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